Question

Question #90a30

Answer 1

`sqrt(3)/2`

Explanation:

If `sin(theta)=1/2`, we know we have a right triangle with hypotenuse of `2` and an opposite side of `1`. We can use Pythagorean's theorem to find the adjacent side:

`a^2+b^2=c^2`
`1^2+b^2=2^2`
`b^2=3`
`b=sqrt(3)`

Since, `cos(theta)=` adjacent/hypotenuse`=sqrt(3)/2`

Answer 2

`cos t = +- sqrt3/2`

Explanation:

`sin t = 1/2` . Find cos t
Use trig identity: `sin^2 t + cos^2 t = 1`
`cos^2 t = 1 - sin^2 t = 1 - 1/4 = 3/4`
`cos t = +- sqrt3/2`
On the unit circle, when `sin t = 1/2`, t could be either in Quadrant 1 or in Quadrant 2. Therefor, there are 2 values of cos x
`cos x = +- sqrt3/2`