Question

Use identities to solve each of the following. Rationalize denominators when acceptable.

Answer 1

-4/5

Explanation:

Since theta is in quadrant II, we can visualize a triangle with two acute angles at (0,0) and (-x, 3). The distance between the two acute angles is 5 (hypotenuse), so using the Pythagorean Theorem, x = sqrt(5^2 - 3^2) = sqrt(16) = 4. Therefore the hypotenuse is 5, opposite is 3, and adjacent is -4.

COS = ADJ/HYP = -4/5

Answer 2

`\cos \theta =-(4)/(5)`

Explanation:

We are given:

`\sin \theta =(3)/(5)`

Then

`\cos^(2) \theta =1-\sin^(2) \theta`

`= 1 - ((3)/(5) )^2`

`= 1 -(9)/(25)`

Then

`\cos^(2) \theta =(16)/(25)`

Then

`\cos \theta =\sqrt{(16)/(25) }\ \ \text{or}\ \ \cos \theta =-\sqrt{(16)/(25) }`

We know that θ is in Quadrant 2.

Then cos θ < 0.

Therefore

`\cos \theta =-\sqrt{(16)/(25) }`

`= -(4)/(5)`