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

1 Answer
Mar 8, 2018

Answer:

#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#