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# 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

Hypotenuse^{2} = Opposite^{2} + Adjacent^{2}

Substituting the values

17^{2} = 15^{2 }+ x^{2}

It can be written as

x^{2} = 17^{2} - 15^{2}

x = √289 - 225

x = √64

x = ±8

So we get

cos θ = ±8/17

Therefore, cos θ = ±8/17.

## 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.

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