Given that cos2y = -7/25 such that y is between 90 and 180 degrees. What is the value of siny?

I want to know if it can be solved by first converting to tan2y and then creating a quadratic equation. Thanks!

1 Answer
Mar 26, 2018

#sin y = 4/5#

Explanation:

Given: #cos 2y = -7/25# , such that #y# is in the second quadrant.

There are a number of ways to solve this problem.

Solve using the double angle identity: #cos 2y = 1-2 sin^2 y#

#1 - 2 sin^2 y = -7/25#

Subtract #1# from both sides:
#-2 sin^2 y = -7/25 - 25/25#

#-2 sin^2 y = -32/25#

Divide by #-2# on both sides:
#sin^2 y =( -32/25)/-2 = -32/25 * -1/2 = 16/25#

Realize that: #" "sin^2 y = (sin y)^2#

Square root both sides:

#sin y = sqrt(16/25) = 4/5#

I wouldn't solve using #tan 2y#, since #tan 2y = (sin 2y)/(cos 2y).#

You don't know #tan 2y, cos y " or " sin 2y = 2 sin y cos y#