Question

Help please ;; i attached the question below

Answer 1

$Answer: \large\boxed{Cos(\theta_{1} )=\frac{84}{85}}$

Step-by-step 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,

$a^2+b^2=c^2$

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

$169+b^2=7225$

$b^2=7056$

$b=\sqrt{7056}$

$b=\pm84$

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,

$Cos(\theta_{1} )=\frac{84}{85}$

See the attached picture: