Question

Given that sin t =(1/4) and that P(t) is a point in the second quadrant, what is the cos of t?

Answer 1

`cos(t) = -sqrt15/4`

Explanation:

Given `sin(t) = 1/4`

Use the identity:

`cos(t) = +-sqrt(1-sin^2(t))`

We are told that `t` is in the second quadrant and we know that the cosine function is negative in the second quadrant, therefore, we chose the negative value for the identity:

`cos(t) = -sqrt(1-sin^2(t))`

Substitute `sin^2(t) = (1/4)^2`:

`cos(t) = -sqrt(1-(1/4)^2)`

`cos(t) = -sqrt(15/16)`

`cos(t) = -sqrt15/4`