If cos θ = 1/6, what are the values of sin θ and tan θ?
Answers
Answer:
Concept :
Use the Pythagoras Theorem and collect the values of hypotenuse , perpendicular and base.Use the formula of sinθ and tanθ✧Thorough solution is provided in the attachment.
Don't hesistate to reach out to me if you have further queries! Have fun studying! <3
The values of [tex]\( \sin \theta \)[/tex] are [tex]\( \frac{\sqrt{35}}{6} \)[/tex] and [tex]\( -\frac{\sqrt{35}}{6} \)[/tex], and the value of [tex]\( \tan \theta \)[/tex] is [tex]\( \sqrt{35} \)[/tex].
Given that [tex]\( \cos \theta = \frac{1}{6} \)[/tex], we need to find [tex]\( \sin \theta \)[/tex] and [tex]\( \tan \theta \)[/tex].
First, we can find [tex]\( \sin \theta \)[/tex] using the Pythagorean identity:
[tex]\[\sin^2 \theta + \cos^2 \theta = 1\][/tex]
Substitute [tex]\( \cos \theta = \frac{1}{6} \)[/tex]:
[tex]\[\sin^2 \theta + \left(\frac{1}{6}\right)^2 = 1\][/tex]
[tex]\[\sin^2 \theta + \frac{1}{36} = 1\][/tex]
[tex]\[\sin^2 \theta = 1 - \frac{1}{36} = \frac{36}{36} - \frac{1}{36} = \frac{35}{36}\][/tex]
[tex]\[\sin \theta = \pm \sqrt{\frac{35}{36}} = \pm \frac{\sqrt{35}}{6}\][/tex]
So, [tex]\( \sin \theta \)[/tex] could be [tex]\( \frac{\sqrt{35}}{6} \)[/tex] or [tex]\( -\frac{\sqrt{35}}{6} \)[/tex].
Next, to find [tex]\( \tan \theta \)[/tex], we use the definition:
[tex]\[\tan \theta = \frac{\sin \theta}{\cos \theta}\][/tex]
Substitute [tex]\( \sin \theta = \pm \frac{\sqrt{35}}{6} \) and \( \cos \theta = \frac{1}{6} \)[/tex]:
[tex]\[\tan \theta = \frac{\frac{\sqrt{35}}{6}}{\frac{1}{6}} = \sqrt{35}\][/tex]
Related Questions
Simplify the expression: (a^4b^5c^6)^3
a^7b^8c^9
a^12b^4c^18
a^4b^5c^6
a^12b^15c^18
Answers
Answer: a^12b^15c^18
Step-by-step explanation:
(good luck in middle school!!)
Elliot wants to open a checking account. He researched checking accounts at different banks near his house. List at least five benefits and/or fees that may differ among the accounts.
Answers
Answer:
it depends, can you put more detail please
Step-by-step explanation:
Answer:
The accounts may differ in minimum balance required, interest rate, ATM fees, overdraw protection, the monthly service fee, and the annual fee.
Step-by-step explanation:
This is urgent, please answer!
Two prisms are shown below.
Which statements about the volumes of the prisms are true? Choose all that apply. I’m
Answers
help please.....A carton holds 42 erasers. Each eraser weighs 3.6 ounces. What is the total weight of the carton?
Answers
Answer:
151.2 ounces
Step-by-step explanation:
You multiply 42 and 3.6
Answer:
151.2 ounces, which is 9.45 pounds.
Step-by-step explanation:
multiply 42 times 3.6
Consider the exponential function
4). What is the value of the growth factor of the function?
COŚ
A. 1/5
B. 1/3
C.5
D.15
Answers
What is the explicit rule that describes the arithmetic sequence shown in the graph
• an= 50+ (n-1) 150
• an= 50+ (n+1) 150
• an= 150+ (n-1) 50
• an= 150+ (n+1) 50
Answers
Answer:
an= 50+ (n-1) 150
Step-by-step explanation:
The second question:
The video game has 24 levels in all. If the pattern shown in the graph continues, how many points would a player get for finding the hidden door on the twenty-fourth level?
3500 points*
The explicit rule that describes the arithmetic sequence will be aₙ = 50 + (n - 1) · 150. Then the correct option is A.
What is an arithmetic sequence?A series of integers called an arithmetic succession or arithmetic chain of events has a fixed difference between the terms.
Let a₁ be the first term and d be a common difference.
Then the nth term of the arithmetic sequence is given as,
aₙ = a₁ + (n - 1)d
The first term is 50 and the common difference is given as,
d = 200 - 50
d = 150
Then the arithmetic sequence is given as,
aₙ = 50 + (n - 1) · 150
The explicit rule that describes the arithmetic sequence will be aₙ = 50 + (n - 1) · 150. Then the correct option is A.
More about the arithmetic sequence link is given below.
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GIVING BRANLIEST!!!
Which ordered pair is the solution to this system of equations?
3x + 5y = 1
x = 2
Group of answer choices
(2, -1)
(-1, 2)
(2, -3)
(-3, 2)
Answers
Consider the equation y=3x-1. Identify the slope and y-intercept and sketch the graph if you can.
Answers
Answer:
Slope: 3, Y-intercept: -1
Step-by-step explanation:
Remember, the slope is always the number before x in this kind of form. The Y-intercept is when x is 0, so when x = 0, y = -1, and that is the Y-intercept
Over which interval is the graph of f(x) = –x2 + 3x + 8 increasing?
a.(–∞, 1.5)
b.(–∞, 10.25)
c.(1.5, ∞)
d.(10.25, ∞)
Answers
Answer:
c
Step-by-step explanation:
cause i said so!
Answer:
The correct answer is A) (-∞ , 1.5)
Step-by-step explanation:
Hope this helps! :)
25x^2-16=25x2-16 completely factor
Answers
if you were to factor 25x^2-16 that would equal (5x-4)(5x+4)
Jane drives 63.84 miles in the morning and 45.9 miles in the afternoon.
How many miles did she drive in all?
Answers
Answer:
109.74 miles.
Step-by-step explanation:
Answer:
109.74 miles.
Step-by-step explanation:
Drag and drop the answer into the box to match each multiplication problem.
Answers
Answer:
The first one is 38. Second one is 38,000. Third one is 3.8
Step-by-step explanation:
They are all powers of 10 (10, 100, 1000 etc) each time adding an extra 0. Just move the decimal point over to the right depending on how many 0's the number has. This only works for power of 10s.
what is the area of the triangle in units
Answers
Answer: Area of the triangle = 14unit²
Step-by-step explanation: The Height of the triangle = 7 unit
The Base of the triangle = 4 unit
∴Area of the triangle = 1/2 bh
= 1/2 × 4 × 7 = 14 units²
Wtjdjdjwjengndjsjsjsndn
Answers
Answer:
median
Step-by-step explanation:
A right triangle has legs that both measure 14 inches. What is the length of its hypotenuse to the nearest whole number?
5 inches
19 inches
20 inches
28 inches
Answers
14^2+14^2=392
square root of 392 is 19.79, round up and you got 20 inches
So, to find this answer, we want to use Pythagorean Theorem!
The formula for this theorem is: a²+b²=c².
· It's important to note that c² is always your hypotenuse, while a and b are your legs.
So, all we need to do is (1) plug in our values, (2) square them, (3) isolate them, and (4) find the square root of our final number!
--------------------------------------------------------------------------------------------------------------
14²+14²=c²
14² = 196
We want to isolate our C, but we can't do that with the squared symbol, so in order to remove a squared symbol, we need to square root both sides.
196 = c²
√196 = 14
C = 14
the bakers at healthy bakery can make 280 bagels in 2 hours. how many bagels can they make in 15 hours? what was the rate per hour?
Answers
Answer:
In 15 hrs they will make 2100 bagels
Step-by-step explanation:
Step one :
Given that it takes
2hrs to make 280 bagel
Hence in
15 hrs they will make x bagels
by cross multiplication
x= (280*15)/2
x= 4200/2=2100 bagels
x= 2100
The area of a rectangle whose perimeter is a fixed 80 feet is given by A=40w - w2 , where w is the width of the rectangle. Determine the width of the rectangle that gives the maximum area. What type of special rectangle is necessary to produce this maximum area? Justify.
Answers
Answer:
Width=20 feet
Since Length=Width=20 feet, the rectangle is a Square.
Step-by-step explanation:
Area, [tex]A=40w - w^2[/tex]
To determine the width of the rectangle that gives the maximum area, we take the derivative of A and solve for its critical point.
[tex]A'=40 - 2w\\$When A'=0\\40-2w=0\\40=2w\\w=20 feet[/tex]
The width of the rectangle that gives the maximum area =20 feet.
Perimeter of a rectangle=2(l+w)
Perimeter of the rectangle=80 feet
2(l+w)=80
2l+2(20)=80
2l=80-40
2l=40
l=20 feet
Since the length and width are equal, the special type of rectangle that produces this maximum area is a Square.
The area of the rectangle is the product of its dimensions
The width that gives the maximum area is 20 feetThe special rectangle is a squareThe area of the rectangle is given as:
[tex]\mathbf{A = 40w - w^2}[/tex]
Differentiate
[tex]\mathbf{A' = 40 - 2w}[/tex]
Set to 0
[tex]\mathbf{40 - 2w = 0}[/tex]
Add 2w to both sides
[tex]\mathbf{ 2w = 40}[/tex]
Divide both sides by 2
[tex]\mathbf{ w = 20}[/tex]
This means that, the width that gives the maximum area is 20 feet
The perimeter of a rectangle is:
[tex]\mathbf{P = 2(l + w)}[/tex]
So, we have:
[tex]\mathbf{80 = 2(l + 20)}[/tex]
Divide both sides by 2
[tex]\mathbf{40 =l + 20}[/tex]
Subtract 20 from both sides
[tex]\mathbf{l = 20}[/tex]
This means that, the length and the width are equal (i.e. 20 ft)
Hence, the special rectangle is a square
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What is the slope of the linear function represented in the table?
A. -7
B.-1/7
C.1/7
D. 7
Answers
Answer:
1/7
Step-by-step explanation:
We can find the slope by
m =(y2-y1)/(x2-x1)
=(1-0)/(0- -7)
(1-0)/(0+7)
1/7
a) 100 degrees
b) 50 degrees
c) 65 degrees
d) 30 degrees
Answers
Answer:
a) 100 degrees
Step-by-step explanation:
EFG + EGD + DGC = 180 since the form a straight line
EGD = 30 since it is a vertical angle to AGB = 30
DGC = 50
Substitute these values in
EFG +30 + 50 = 180
Combine like terms
EFG +80 = 180
Subtract 80 from each side
EFG +80-80 = 180-80
EFG =100
Marble Slab Creamery is creating a cone-shaped paper wrapper for its new green Baby Yoda waffle cone. The wrapper should have a radius of 5 cm and a slant height of 10 cm. One location wants to offer the cones a weekend earlier, so they plan to make the cone-shaped wrappers for first 25 waffle cones sold that Saturday. About how many square cm of wrapper paper will they need?
Answers
Answer:
3927 square cm
Step-by-step explanation:
We want to find the area of the lateral part of the cone with radius 5 and slant height 10. The equation needed is: L = πrl, where r is the radius and l is the slant height. Plug the given values in:
L = πrl
L = π * 5 * 10 = 50π square cm
We want 25 of these, so multiply 50π by 25:
50π * 25 ≈ 3926.99 square cm ≈ 3927 square cm
Answer:
3,925 cm²
Step-by-step explanation:
Wrapper area is equal to the surface area
Curved surface area of one cone:
(pi × r × s)
3.14 × 5 × 10
157
For 25 cones:
25 × 157
3925 cm²
find the value of X
Answers
Answer:
[tex]x=\sqrt{55}[/tex] (B.)
Step-by-step explanation:
Equation:
[tex]a^{2} +b^{2} = c^{2}[/tex]
[tex](3^{2} )+(x^{2})=(8^{2})[/tex]
[tex]9+x^{2} =64[/tex]
[tex]x^{2} = 55[/tex]
[tex]\sqrt{x^{2} } =\sqrt{55}[/tex]
[tex]x=\sqrt{55}[/tex]
Sharon graphed the formula for converting weight from kilograms to pounds.
A line graph titled Conversion Chart has Pounds on the x-axis and Kilograms on the y-axis. 33 pounds is 15 kilograms, 88 pounds is 40 kilograms.
If an item weighs 45 kilograms, what is its weight in pounds?
A. 20
B.63
C.90
D. 99
Answers
Answer:
Option "D" is the correct answer to the following question.
Step-by-step explanation:
Given:
On x-axis ⇒ 33 pounds = 15 kilograms
On y-axis ⇒ 88 pounds = 40 kilograms.
Find:
45 kilograms in pounds = ?
Computation:
On x-axis
Weight in pounds = (33 pounds / 15 kilograms)45 kilograms
Weight in pounds = 99 pound
On x-axis
Weight in pounds = (88 pounds / 40 kilograms)45 kilograms
Weight in pounds = 99 pound
Answer:
d or 99
Step-by-step explanation:
i got a 100
A right triangle has a height of 27 inches
and a base of 30 inches. What is the area
of the triangle?
Answers
Answer:
405 [tex]inches^{2}[/tex]
Step-by-step explanation:
Area of a triangle = [tex]\frac{1}{2}[/tex] Base * Height
[tex]\frac{1}{2}[/tex] * 30* 27 = 405 [tex]inches^{2}[/tex]
The formula for area of a triangle is 1/2Bh. One half of the area of the base times height, because base times height is a square and triangles are half a square. Let's solve for the area now.
A=1/2Bh
Plug in our information
A=1/2(30)(27)
Multiply parentheses.
A=1/2(810)
Multiply by 1/2 or divide by two.
A=405
The area of the triangle is 405 inches squared.
The length of one of the congruent legs must be greater than what value? x > feet
Answers
Answer:7
Step-by-step explanation:
half of 14
Answer:
7
Step-by-step explanation:
3.5 x 2
Help pleaseeee
A rectangle has an area of 58.1 square meters and a height of 7 meters. What is the length
of the base?
Answers
Answer:
8.3 meters
Step-by-step explanation:
58.1 / 7 =8.3
Answer:
8.3 meters
Step-by-step explanation:
A rectangle's area is solved by multiplying length x height.
The area is 58.1 square meters, while the height is 7 meters. Divide:
58.1/7 = 8.3
8.3 meters is the length of the rectangle.
~
ANSWER ASAP! Thank you for your help! If you don’t see what it says on the end it says “A brick has a mass of”
Answers
Answer:
1.32
Step-by-step explanation:
.6*2.2
A right triangle has a hight of 13 cm and a base of 16.4 cm what is the area of the triangle
Answers
Answer:
It would be 213.2
Step-by-step explanation: You multiply 13 and 16.4 to find the area. Let me know if im wrong.
Answer:
106.6 cm
Step-by-step explanation:
I multiplied the two given values and using the formula A=1/2bh I then multiplied it by 1/2 and got 106.6. Hope this helps! If you are still confused, please comment!
About 24% of people who get their feet examined are found to have bunions. What is the probability of a podiatrist examining six
people until he finds the first patient who has bunions?
(0.24)
(0.24)*(0.76)
(0.76) (0.24)
(0.76)
1 - (0.24)
Answers
Answer:
0.76)5(0.24)1
Step-by-step explanation:
The probability of a podiatrist examining six people until he finds the first patient who has bunions is [tex](0.76)^5[/tex] (0.24).
What is Probability?Probability refers to potential. A random event's occurrence is the subject of this area of mathematics.
The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events.
The degree to which something is likely to happen is basically what probability means.
We have,
24% of people who get their feet examined are found to have bunions.
let p= 24%= 0.24
and, q= 1-p = 1-0.24 = 0.76
When he examines 6 people before he sees a patient with an bunions, the event is represented as:
P = ([tex]q^5[/tex]) p
= [tex](0.76)^5[/tex] (0.24)
= 0.2535525376 (0.24)
= 0.060852609024
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There are 12 inches in one foot and 3 feet in one yard. How many inches are in 2 yards
Answers
One Foot: 12 inches
One Yard: 3 Feet
3 x 12 = 36 inchest
One Yard: 36 inches
36 x 2 = 72
Therefore there are 72 inches in 2 yards.
The study of ___ is called kinematic.
Answers
Answer:
motion without regard to the forces or energies that may be involved
Step-by-step explanation:
Answer:
The study of motion is called kinematic