Question

Suppose that sin a=15/17 and 0π/2 find the values of other trigonometric functions?

Answer 1

Given that sin a = 15/17 with a between 0 and π/2, we calculate other trigonometric functions using the Pythagorean identity and their definitions. We determine that cos a = 8/17, tan a = 15/8, cot a = 8/15, sec a = 17/8, and csc a = 17/15.

Step-by-step explanation:

If we know that sin a = 15/17 and a is in the interval (0, π/2), we can find the values of the other trigonometric functions using the Pythagorean identity and the definitions of the trigonometric functions.

First, we'll find cos a. Remembering that sin2 a + cos2 a = 1, we can solve for cos a:

1. sin2 a = (15/17)2
2. cos2 a = 1 - sin2 a = 1 - (225/289)
3. cos2 a = 64/289, so cos a = ±8/17
4. Since a is in the first quadrant, cos a > 0, therefore cos a = 8/17

Then, we can find tan a and cot a by their definitions:

1. tan a = sin a / cos a = (15/17) / (8/17) = 15/8
2. cot a = 1 / tan a = 8/15

Finally, using the reciprocal identities:

1. sec a = 1 / cos a = 17/8
2. csc a = 1 / sin a = 17/15