Final answer:
To find cos(sin^-1(15/17)), a right triangle is considered where the opposite side is 15, and hypotenuse is 17. Applying the Pythagorean theorem gives the adjacent side as 8. Thus, the exact value is cos(sin^-1(15/17)) = 8/17. a) 8/17
Step-by-step explanation:
The question is asking for the exact value of cos(sin-1(15/17)). To find this, imagine a right triangle where the opposite side to the angle is 15 units and the hypotenuse is 17 units. We can then use the Pythagorean theorem to calculate the adjacent side, which is the side we need to find the cosine value.
Let the adjacent side be 'x'. According to the Pythagorean theorem:
- x2 + 152 = 172
- x2 + 225 = 289
- x2 = 289 - 225
- x2 = 64
- x = 8 (since x is positive in the context of a right triangle)
Now we can find the cosine:
- cos(sin-1(15/17)) = adjacent/hypotenuse
- = 8/17