If sin θ = 15 over 17, use the Pythagorean identity to find cos θ.

Solution:

It is given that

sin θ = 15/17

Using the trigonometric identities

sin θ = opposite/ hypotenuse

cos θ = adjacent/ hypotenuse

tan θ = opposite/ adjacent

Here hypotenuse = 17

Opposite = 15

Assume adjacent = x

Using the pythagorean identity

Hypotenuse² = Opposite² + Adjacent²

Substituting the values

17² = 15² + x²

It can be written as

x² = 17² - 15²

x = √289 - 225

x = √64

x = ±8

So we get

cos θ = ±8/17

Therefore, cos θ = ±8/17.

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If sin θ = 15 over 17, use the Pythagorean identity to find cos θ.

Summary:

If sin θ = 15 over 17, using the pythagorean identity cos θ = ±8/17.