Question

1. which trig ratio is represented for angle a?
2. which trig ratio is represented for angle b?
3. identify the following trigonometric ratios.

sin b =
sin a =
cot b =
cos a =
tan b =
tan a =

Explanation:

Step1: Recall trig - ratio definitions

In a right - triangle, $\sin\theta=\frac{\text{opposite}}{\text{hypotenuse}}$, $\cos\theta=\frac{\text{adjacent}}{\text{hypotenuse}}$, $\tan\theta=\frac{\text{opposite}}{\text{adjacent}}$, $\cot\theta=\frac{\text{adjacent}}{\text{opposite}}$.
For the triangle with sides 8, 15, and 17 (where $8^{2}+15^{2}=64 + 225=289 = 17^{2}$, so it's a right - triangle).

Step2: Find $\sin B$

For $\angle B$, the opposite side is 15 and the hypotenuse is 17. So $\sin B=\frac{15}{17}$.

Step3: Find $\sin A$

For $\angle A$, the opposite side is 8 and the hypotenuse is 17. So $\sin A=\frac{8}{17}$.

Step4: Find $\cot B$

For $\angle B$, the adjacent side is 8 and the opposite side is 15. So $\cot B=\frac{8}{15}$.

Step5: Find $\cos A$

For $\angle A$, the adjacent side is 15 and the hypotenuse is 17. So $\cos A=\frac{15}{17}$.

Step6: Find $\tan B$

For $\angle B$, the opposite side is 15 and the adjacent side is 8. So $\tan B=\frac{15}{8}$.

Step7: Find $\tan A$

For $\angle A$, the opposite side is 8 and the adjacent side is 15. So $\tan A=\frac{8}{15}$.

Answer:

$\sin B=\frac{15}{17}$, $\sin A=\frac{8}{17}$, $\cot B=\frac{8}{15}$, $\cos A=\frac{15}{17}$, $\tan B=\frac{15}{8}$, $\tan A=\frac{8}{15}$