Use the given function value(s), and trigonometric identities (including the cofunction identities), to find the indicated trigonometric functions.
Cos θ

B)
C)
D)

Question

Use the given function value(s), and trigonometric identities (including the cofunction identities), to find the indicated trigonometric functions. ​  ​
Cos θ
​
B)​ 
C)​ 
D)​

Quizplus · Accepted Answer

We know that cosine is adjacent/hypotenuse, so we can use the Pythagorean theorem to find the opposite side.
opposite = √(hypotenuse^2 - adjacent^2) = √(1 - (11/13)^2) = √(1 - 121/169) = √(48/169)
Now we can use the sine function to find sin θ:
sin θ = opposite/hypotenuse = √(48/169)/13 = √(48)/169
Using the identity cos^2 θ + sin^2 θ = 1, we can find cos θ:
cos θ = ±√(1 - sin^2 θ) = ±√(1 - 48/169) = ±√(121/169) = ± 11/13. Since cosine is positive in the second quadrant where sin is positive, we choose positive 11/13.

Use the Given Function Value(s), and Trigonometric Identities (Including the Cofunction