Question

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i attached the question below

Answer 1

`Answer: \large\boxed{Cos(\theta_(1) )=(84)/(85)}`

Explanation:

Thinking about a triangle in Quadrant IV, we can imagine sin as opposite/hypotenuse. Therefore, the hypotenuse is 85 and the opposite angle is -13. To find the adjacent angle, we use the pythagorean theorum,

`a^2+b^2=c^2`

`-13^2+b^2=85^2`

`169+b^2=7225`

`b^2=7056`

`b=√(7056)`

`b=\pm84`

Taking only the positive number, the adjacent angle is 84

Now that we have all 3 sides, we can find the cosine.

Cosine is adjacent/hypotenuse

Therefore,

`Cos(\theta_(1) )=(84)/(85)`

See the attached picture: