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Question 1 of 3
Find tanθ given the following
Write fractions in the format “a/b”
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First, draw a triangle that satisfies sinθ=2129 (the sign is disregarded in this process)
Using the triangle above, use the Pythagoras’ Theorem to solve for x
a2+b2 |
= |
c2 |
Pythagoras’ Theorem |
212+x2 |
= |
292 |
Substitute values |
441+x2 |
= |
841 |
441+x2 -411 |
= |
841 -411 |
Subtract 441 from both sides |
x2 |
= |
400 |
√x2 |
= |
√400 |
Get the square root of both sides |
x |
= |
±20 |
Recall the right triangle to find the value of tanθ
tanθ |
= |
oppositeadjacent |
|
|
= |
2120 |
Remember that tanθ=sinθcosθ
Since sinθ is negative and cosθ is positive, tanθ is negative
Therefore, tanθ=-2120
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Question 2 of 3
Find cosθ given the following
Write fractions in the format “a/b”
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First, draw a triangle that satisfies sinθ=35 (the sign is disregarded in this process)
Using the triangle above, use the Pythagoras’ Theorem to solve for x
a2+b2 |
= |
c2 |
Pythagoras’ Theorem |
32+x2 |
= |
52 |
Substitute values |
9+x2 |
= |
25 |
9+x2 -9 |
= |
25 -9 |
Subtract 9 from both sides |
x2 |
= |
16 |
√x2 |
= |
√16 |
Get the square root of both sides |
x |
= |
±4 |
Recall the right triangle to find the value of cosθ
cosθ |
= |
adjacenthypotenuse |
|
|
= |
45 |
Identify the appropriate quadrants in the unit circle to find the sign of cosθ
In the fourth quadrant, cosθ is positive
Therefore, cosθ=45
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Question 3 of 3
Find sinθ given the following
Write fractions in the format “a/b”
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First, draw a triangle that satisfies cosθ=513 (the sign is disregarded in this process)
Using the triangle above, use the Pythagoras’ Theorem to solve for x
a2+b2 |
= |
c2 |
Pythagoras’ Theorem |
y2+52 |
= |
132 |
Substitute values |
y2+25 |
= |
169 |
y2+25 -25 |
= |
169 -25 |
Subtract 25 from both sides |
y2 |
= |
144 |
√y2 |
= |
√144 |
Get the square root of both sides |
y |
= |
±12 |
Recall the right triangle to find the value of sinθ
sinθ |
= |
oppositehypotenuse |
|
|
= |
1213 |
Identify the appropriate quadrants in the unit circle to find the sign of cosθ
In the third quadrant, sinθ is negative
Therefore, sinθ=-1213