The point (1, −1) is on the terminal side of angle θ, in standard position. What are the values of sine, cosine, and tangent of θ? plz show me how u got the answer
Answers
The two sides, AB and BC are equal
By Pythagoras, we find the length of AC = [tex] \sqrt{1^+1^} [/tex] = [tex] \sqrt{2} [/tex]
Using the sin ratio ⇒ sin θ = opposite/hypotenuse, we have
[tex]sin(45)= \frac{1}{ \sqrt{2} }= \frac{ \sqrt{2} }{2} [/tex]
Using the cos ratio ⇒ cos θ = adjective/hypotenuse, we have
[tex]cos(45)= \frac{1}{ \sqrt{2} }= \frac{ \sqrt{2} }{2} [/tex]
Using the tan ratio ⇒ tan θ = opposite/adjective, we have
[tex]tan(45)= \frac{1}{1}=1 [/tex]
The values of sine, cosine, and tangent for angle θ, where (1, -1) is on its terminal side, are sin(θ) = -1, cos(θ) = 1, and tan(θ) = -1, knowing that the point lies in the fourth quadrant.
To find the values of the sine, cosine, and tangent of an angle θ where the point (1, -1) is on its terminal side, we first recognize that this point lies in the fourth quadrant of the coordinate system. In this quadrant, cosine is positive, and sine and tangent are negative.
The point (1, -1) gives us the x and y coordinates on the Cartesian plane, which correspond to the lengths of the adjacent side and the opposite side of the right-angle triangle formed by the radius (hypotenuse) from the origin to the point, and the axes. Assuming we're dealing with a unit circle (which has a radius of 1), we can directly use the coordinates (1, -1) to find the cosine and sine:
cos(θ) = x = 1sin(θ) = y = -1tangent (θ) = y/x = -1/1 = -1Hence, for angle θ, cos(θ) is 1, sin(θ) is -1, and tan(θ) is -1.
Related Questions
(01.07)
Name the algebraic property demonstrated in the example below:
(2 + x) + y = 2 + (x + y) (1 point)
Commutative Property of Addition
Associative Property of Addition
Distributive Property
Transitive Property
Answers
We basically have 2+x+y on each side. The difference is the use of parenthesis in different places. With addition, we can add in any order we want and that includes grouping terms as well. For example
(2+3)+5 = (5)+5 = 5+5 = 10
2+(3+5) = 2+(8) = 2+8 = 10
So that's why in general (2+x)+y = 2+(x+y) is true for all real numbers x and y.
Partway through the season, a basketball coach promises his team that he will take them to a water park if they reach 1,000 points as a team by the end of the season. So far, they have scored 424 points. There are 9 games left in the season. Fill in the values for a, b, and c to create an equation that can be used to find the average number of points, x, the team needs to score in each of the remaining games to meet their goal.
Answers
n = 1000 - 424 = 576
If we are to determine the number of points each game, we divide 576 by 9. That is,
x = 576 / 9 = 64
ANSWER: 64 points/ game
Find the distance between the points 1,4 and (-2,-1
Answers
The graph of a combination of line segments that passes the vertical line test is a ?
Answers
Nonlinear function (A)
The graph of a combination of line segments that passes the vertical line test is a Non Linear function.
What is vertical line test?The vertical line test states that a graph represents a function if and only if all vertical lines intersect the graph at most once.
The vertical line check is a graphical approach of determining whether or not a curve inside the aircraft represents the graph of a function by means of visually examining the variety of intersections of the curve with vertical lines.A vertical line intersects with them only once, making them features.Parabolas that face upward and downward are capabilities.They may be functions because a vertical line intersects the curve no extra than once.
If a vertical line intersects a curve on an xy-plane greater than once then for one price of x the curve has multiple value of y, and so, the curve does now not represent a function. If all vertical lines intersect a curve at most once then the curve represents a function.
The vertical line take a look at helps to find it a given curve represents a function or now not. If the vertical line cuts the graph of the equation at simplest one factor, then it's miles a characteristic, and if cuts the graph of the characteristic at a couple of point, then it does not constitute a characteristic. A vertical form is a shape with layers stacked on top of every other, with a fixed layer top, for instance a spherical tower where the radius corresponds to the datapoint.
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solve the system of equations solve for x
y=6x+12
solve for y
y=x+47
Answers
To solve the system of equations xy = 6x + 12 and yy = x + 47, we can rearrange the equations, isolate one variable, and substitute it into the other equation. Then, solve for the variables. The solution is x = 282 / (270 - y) and y = (270 - xy) / 6.
Explanation:To solve the given system of equations,
xy = 6x + 12
yy = x + 47
We can start by rearranging the equations:
xy - 6x = 12
yy - x = 47
Next, we can isolate one variable in terms of the other variable and substitute it into the other equation:
x = (yy - 47)
xy - 6(yy - 47) = 12
Simplifying the equation:
xy - 6yy + 282 = 12
Combining like terms:
-6yy + xy = -270
Now, we can solve this equation for y in terms of x:
y = (270 - xy) / 6
Re-substituting the value of y back into one of the original equations:
(270 - xy) / 6 * x = 47
Simplifying and solving for x:
270x - xy = 282
x(270 - y) = 282
x = 282 / (270 - y)
So, the solution to the system of equations is:
x = 282 / (270 - y)
y = (270 - xy) / 6
Which line is a line of symmetry for this regular polygon?
line g
line h
line i
Answers
Line G is the line of symmetry here because if you used that line to cut the shape in half, it will be the exact same size and shape.
Line g is a line of symmetry of this regular polygon.
We have regular polygon as shown in the figure.
We have to determine which line is a line of symmetry for this regular polygon.
What do you understand by the Symmetry of any plane figure?A plane figure is symmetric about a line if it is its own image when flipped across the line. The reflection line is the line of symmetry.
According to the question, we have a Regular Polygon.
According to the concept of Symmetry of any plane figure -
if we fold this polygon about the line g then both the sides will overlap.
The lines i and h do not fulfill this condition.
Hence, line g is a line of symmetry of this regular polygon.
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The average height of a female draft is 4.6 meters. Was her height in centimeters.
Answers
Final answer:
To convert the average height of a female giraffe from meters to centimeters, multiply 4.6 meters by 100, resulting in 460 centimeters.
Explanation:
To convert the average height of a female giraffe from meters to centimeters, we need to use the conversion factor where 1 meter is equivalent to 100 centimeters. If the average height is 4.6 meters, then we need to multiply this value by 100 to find the height in centimeters
Step-by-step calculation
This conversion process, from meters to centimeters, simplifies the representation of the average height of a female giraffe. Utilizing the conversion factor, where 1 meter equals 100 centimeters, the calculated result of 460 centimeters provides a more practical and commonly used metric. Such conversions are valuable for ensuring consistency in measurement units and facilitating communication across different contexts, enhancing our understanding of the physical dimensions of giraffes in a more accessible manner.
Perform the indicated operation.
4/11 x 10/8
Answers
0.36 x 1.25 = 0.45
or
4/11 x 10/8 = 5/11
To solve the operation 4/11 x 10/8, multiply the numerators and denominators separately. The result is 0.45454545454.
Perform the indicated operation: 4/11 x 10/8
Multiply the numerators: 4 x 10 = 40
Multiply the denominators: 11 x 8 = 88
The result is 40/88 = 0.45454545454
Figure TQRS ~ BCDE. What are the pairs of congruent angles?
Answers
Angle T ~ angle B
Angle Q ~ Angle C
Angle R ~ Angle D
Angle S ~ Angle E.
Additionally, in this particular case, it also happens that two angles in the same figure are congruents: angle T ~ angle Q, which implies angle T ~ angle Q ~ angle B ~ angle C
Answer:
R ~ D,
S ~ E,
T ~ B, and
Q ~ C
The folding chair can be set in different positions that change the angles formed by its parts. As angle 1 increases, how does the relationship change between the back of the chair and the front leg of the chair?
A. As the measure of increases, the distance between the back of the chair and the front leg of the chair increases.
B. As the measure of increases, the distance between the back of the chair and the front leg of the chair decreases.
C. As the measure of increases, the distance between the back of the chair and the front leg of the chair remains constant.
Answers
Final answer:
In the context of a folding chair, as angle 1 (between the backrest and the seat) increases, the distance between the back of the chair and the front leg correspondingly increases due to the lever-like movement of the backrest.
Explanation:
When considering the geometry of a folding chair and the angles formed by its parts, it's important to visualize the chair as a system of linked levers. As angle 1 increases, which is the angle between the backrest of the chair and the seat, the relationship between the back of the chair and the front leg changes. If we assume that the front leg stays still and the back of the chair moves backward to increase the angle, the distance between the back of the chair and the front leg increases. This movement can be seen as the backrest acting like a lever, where increasing the angle effectively moves the lever away from the pivot point at the front leg.
Therefore, the correct answer in the context of a folding chair is: A. As the measure of angle 1 increases, the distance between the back of the chair and the front leg of the chair increases.
What’s the temperature difference between -5 degrees and 25 degrees?
A.20 degrees
B.25 degrees
C.30 degrees
D.35 degrees
Answers
difference between -5 and 25 is
25 + 5 = 30 degrees
answer is C.
What is 31/8 as a decimal
Answers
Hope this helps!!
How do you find how many solutions a system of equations has?
Answers
1. In ∆ABC the angle bisectors drawn from vertexes A and B intersect at point D. Find ∠ADB if: m∠A = α , m∠B = β
2.Angle bisectors of the angles ∠A and ∠B of a triangle ∆ABC intersect each other at point M. Find m∠AMB, if m∠A = 58°, m∠B = 96°.
Answers
The measure of an angle formed by the intersection of two angle bisectors in a triangle is the semisum of the two angles being bisected. So, in both situations, ∠ADB and ∠AMB will be (α + β)/2.
Explanation:In a triangle, the angle formed by the intersection of two angle bisectors is always equal to the semisum of the two angles being bisected. Therefore, in ∆ABC, the measure of ∠ADB (∠ formed by the intersection of the bisectors from ∠A and ∠B) will be (α + β)/2.
For example, if angle A is 40° (let's represent it by α) and angle B is 60° (let's represent it by β), the ∠ADB will be (40 + 60) / 2, which equals 50°.
In the second problem, the measure of ∠AMB will also be equal to the average of ∠A and ∠B, so m∠AMB = (58° + 96°) / 2 = 77°. This rule applies to any triangle ABC, regardless of the type of triangle.
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Answer:
Hi, sorry, but my computer is glitching and I can't put in the answer for some reason.... I'm REALLY sorry...
Step-by-step explanation:
Mark shoots arrows at a target and hits the bull's-eye about 40% of the time. find the probability that he hits the bull's-eye on the fourth shot
Answers
The probability of Mark hitting the bull's-eye on the fourth shot, assuming he misses the first three times, is 8.64%. This is calculated as the product of the probabilities of each event occurring independently.
Explanation:This is indeed a problem related to probability, particularly, this pertains to the concept of an independent event in statistics. Mark's success in shooting an arrow accurately to the target is an independent event because the outcome of one shot doesn't affect the outcome of other shots.
In Mark's case, he hits the bull's-eye about 40% of the time, i.e. his success rate P(Success) is 0.40 and his failure rate P(Failure) is 0.60. Since the question asked about the probability of him hitting the bull's-eye on the fourth shot, we should look at the first three shots being failures and only the fourth being a success.
This leads us to the calculation: P(FFFH) = P(F) x P(F) x P(F) x P(H) = (0.60)*(0.60)*(0.60)*(0.40) = 0.0864 or 8.64% chance.
So, there's an 8.64% chance that Mark will hit the bull's-eye on the fourth shot given that he misses the first three.
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The probability that Mark hits the bull's-eye on his fourth shot, given he typically hits the bull's-eye 40% of the time, is 0.0864 or 8.64%
Explanation:The problem is about the probability that Mark hits the bull's-eye on the fourth shot given that he hits the bull's-eye about 40% of the time. In these cases, for the first three shots, he should not hit the bull's-eye (probabilty of 60%) and on the fourth trial, he should hit the bull's-eye (probability of 40%). Therefore, we multiply the individual probabilities together to find the answer.
Step 1: Find the probability that he does not hit the bull's-eye in the first three trials. This is (0.6)*(0.6)*(0.6) = 0.216.
Step 2: Find the probability that he hits the bull's-eye on the fourth trial. This is simply 0.4.
Step 3: Multiply the two probabilities together to find the final answer. This gives us 0.216*0.4 = 0.0864.
So, the probability that Mark hits the bull's-eye on the fourth shot is 0.0864, or 8.64%.
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Simplify. 7/3+3(2/3−1/3)^2
All of these are fractions except the three and the exponent
Answers
7/3 +3(2/3 -1/3)^2 =
2/3 -1/3 = 1/3 now you have
7/3 +3(1/3)^2
1/3^2 = 1/9
7/3 +3(1/9)
3*1/9 = 1/3
7/3 + 1/3 = 8/3, which can be changed to 2 2/3
Greta is opening a savings account. She starts with $100 and plans to add $59 each week. Write an equation she can use to calculate the amount of money she will have after any number of weeks. How much money will she have after 1 year?
Answers
F (x)=100+59x
Where
F amount of money she will have ?
X number of weeks in a year 52 weeks
F (52)=100+59×52
F (52)=3,168
Hope it helps!
Angela enjoys swimming and often swim a at a steady pace to burn calories. At this pace, Angela can swim 1,700 meters in 40 minutes. What is Angela's unit rate?
Answers
all you do is multiply 17 ×4 then with that product you got you just add the 3 0's
What are the dimensions of the rectangle of greatest area that can be formed with 200 feet of fence?
Answers
Dimensions are 50 feet by 50 feet.
Let the length = x
the width = y
So the perimeter = 2(x+y)=200
or, x+y=100
or, y=100-x
So the area is = A = xy = x(100-x).
For greatest area A' = 0 and A" < 0.
[tex]A= x(100-x)\\A=100x-x^2\\A'=100-2x\\A''=-2[/tex]
We set A'=0 to find x.
[tex]100-2x=0\\2x=100\\x=50[/tex]
For x=50, A"=2 < 0
It means for x=50, y=100-50=50 the rectangle will have the greatest area.
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How much pasta will each person get if 6 people share 2/3 lb of pasta equally?
Answers
6 x 2/3
Each person would get 1/9 lb of pasta if 6 people were to share 2/3 lb of pasta equally.
Explanation:In the given question, 6 people are sharing 2/3 lb of pasta equally. This implies that we are performing an operation of division. You would divide 2/3 by 6 to find out how much each person gets. Here's how you can do it:
First, write the fraction 2/3 as the division of two numbers 2 divided by 3. Now divide 2 by 6 which equals 1/3. Now, divide 1/3 by 3. Therefore, each person will get 1/9 lb of pasta. Learn more about division here:
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Find the slope of each of the lines below:
Answers
slope formula : (y2 - y1) / (x2 - x1)
(-2,-5)....x1 = -2 and y1 = -5
(6,5).....x2= 6 and y2 = 5
now we sub and solve
slope = (5 - (-5) / (6 - (-2) = (5 + 5) / (6 + 2) = 10/8 reduces to 5/4 <=
Solve the system of equations using matrices. Use Gaussian elimination with back-substitution.
x + y + z = -5
x - y + 3z = -1
4x + y + z = -2
Answers
Solution in file jointed.
==================
What must you add to the expression x2+bxx2+bx to complete the square?
Answers
We are given the incomplete expression:
x^2 + b x
Now to complete the square, we need to add the square of the half of b, that is:
(b / 2)^2
or
b^2 / 4
Therefore the complete expression is:
x^2 + b x + (b^2 / 4)
Which example supports the given conjecture? the sum of two odd numbers is an even number.
a. 0 + 3 = 3
b. 2 + 6 = 8
c. 5 + 7 =12
d. 4 + 9 = 13?
Answers
Suppose that you have the option to buy an item with either cash or credit. Under which condition would you use credit?
Answers
Answer:
By having or building a good credit history.
Step-by-step explanation:
When an item is to bought by you on credit , for you to have or build a good credit history , Buying something with credit means that you are buying something with money you don't have at that very time
Later on, you will have to give back this money borrowed to a person,an interest will be paid for lending it.
f (x)=4x-7 when f (x)=8
Answers
4x-7=8
Add 7 to both sides
4x= 15
Divide both sides by 4
x=15/4
Final answer: x=15/4
if f(4)=183.07 when r=0.04 for the function f(t)=Pe* then what is the appropriate value of P?
Show work please
Answers
when t = 4 the value of the function is 183.07.
Substitute those values and the value for r into the formula.
[tex]183.07=Pe^{0.04*4}[/tex]
0.04 x 4 = 0.16
Divide both side by [tex]e^{0.16}[/tex]
[tex]\frac{183.07}{e^{0.16}}=P[/tex]
P is approximately 156.002
_____________________________________________
If "P" is the "prinicipal amount" in dollars and cents, we would round up to the nearest hundredth, or "cent" (percentage of a dollar); and the answer would be:
" $155.00 " . Otherwise, if we are talking about population, we would round to the nearest hundredth, to maintain 5 (five) significant figures, and the answer would be: " 155.00" {in some cases, "155" would suffice} .
___________________________________________________________
Explanation:
________________________________________________________
f(t) = P*e^(r*t) ;
f(4) = P*e^(0.04 * 4) ;
Given: " f(4) = 183.07 ";
Calculate: (r*t = 0.04 * 4 = 0.16) ;
Rewrite the equation; substituting: "183.07" for "f(4)" ; {i.e., for "f(t)" } ;
and substituting: "0.16" for "(0.04* 4)" ; {i.e. for "(r*t) } ;
_______________________________________________________
→ Since we want to solve for: "P" ;
_____________________________________________
→ (183.07) = P * e^(0.16) ;
_____________________________________________
↔ P * e^(0.16) = (183.07) ;
______________________________________________
→ Divide EACH SIDE of the equation by: { "e^(0.16)" } ; to isolate "P" on one side of the equation; and to solve for "P" ;
______________________________________________
→ { P * e^(0.16) } / { e^(0.16) } = { 183.07 }/ { (e^(0.16) } ;
______________________________________________
→ P = { 183.07 }/ { (e^(0.16) } ;
______________________________________________
NOTE: " e^(0.16) = 1.17351087099 " ;
______________________________________________
→ P = (183.07)/ (1.17351087099) ;
______________________________________________
→ P = 156.001963446
Now, assuming "P" is the "prinicipal amount" in dollars and cents, we would round up to the nearest hundredth, or "cent" (percentage of a dollar); and the answer would be: $ 155.00 . Otherwise, if we are talking about population, we would round to the nearest hundredth, to maintain 5 (five) significant figures, and the answer would be: " 155.00 " (in some cases, simply "155" would be sufficient).
________________________________________
Hope this helps!
________________________________________
ALGEBRATIC EXPRESSIONS HELP
the product of 4 and a number is increased by 7
Answers
product means multiply
increased by means add
so product of 4 and a number would be 4n
than add 7
so you have 4n+7
You decide to put $100 in a savings account to save for a $3,000 down payment on a new car. If the account has an interest rate of 2% per year and is compounded monthly, how long does it take you to earn $3,000 without depositing any additional funds?
Answers
Answer:
170.202 years
Step-by-step explanation:
From the compound interest formula, that has interest rate in times per year but compounds monthly we have
[tex]A=P(1+\frac{r}{n})^{nt}[/tex]
A is the amount you want to save, P is the principal (what you put down, in this case 100), r is the anual interest rate, n is 12 i.e the times it compounds, and t is the amount of years it will take. So we have data for all variables but t.
Solving for t we have
[tex]\frac{A}{P}=(1+\frac{r}{n})^{nt}[/tex]
taking logs
[tex]log(\frac{A}{P})=nt \,log(1+\frac{r}{n})[/tex]
finally
[tex]t = \frac {log(\frac{A}{P}) }{ n[log(1 + \frac{r}{n})]}[/tex]
replacing and calculating we get t=170.202
What is the x coordinate in the solution of the system of equations y =-2/3x and 4x - 9y =-40
Answers
y = -2/3 x
4x - 9y = -40
Substitute by the first equation in the second as follows:
4x - 9(-2/3 x) = -40
4x + 6x = -40
10x = -40
x = -4
The x-coordinate in the solution of the given system of equations is -4.
Explanation:The x-coordinate in the solution of the given system of equations can be found by substituting the value of y from one equation into the other equation and solving for x. Let's solve the system of equations:
Start with the equation y = -2/3x. Substitute this into the second equation:
4x - 9(-2/3x) = -40
Now simplify and solve for x:
4x + 6x = -40
10x = -40
x = -4
So, the x-coordinate in the solution of the system of equations is -4.
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