Question

Find the exact value of cos (theta) for an angle (theta) with sin (theta) = 3/8 and with its terminal side in Quadrant I.

a. 5/8

b. - sqrt(55)/8

c. 8/3

d. sqrt(55)/8

Answer 1

d

Explanation:

Cos²theta = 1 - sin²theta

= 1 - (3/8)² = 55/64

Cos theta = sqrt(55)/8

Positive because Quadrant 1

Answer 2

`(√(55))/(8)`

Explanation:

`\sin(\theta)=(3)/(8)` is given.

We are also given that
`\theta`'s angle terminates in quadrant one which means all 6 trig ratios are positive there.

We will use Pythagorean Identity:
`\sin^2(\theta)+\cos^2(\theta)=1`.

`((3)/(8))^2+\cos^2(\theta)=1`

`(9)/(64)+\cos^2(\theta)=1`

`\cos^2(\theta)=1-(9)/(64)`

`\cos^2(\theta)=(64-9)/(64)`

`\cos^2(\theta)=(55)/(64)`

`\cos(\theta)=\pm \sqrt{(55)/(64)}`

`\cos(\theta)=(√(55))/(8)`.