If cos y = -4/5 when 90°≤ y ≤ 180° what is the value of cos 2y?
quadrant 2
cos 2y = 1 - 2 sin^2 y
but sin y = 3/5 (3 4 5 triangle)
cos 2 y = 1 - 2 (3/5)
= 1 - 6/5
= -1/5
last 3 lines should be
cos (2y) = 1 - 2(3/5)^2
= 1 - 18/25 = 7/25 or .28
Whoops, thank you
To find the value of cos 2y, we can use the double-angle identity for cosine:
cos(2y) = 2cos^2(y) - 1
Given that cos y = -4/5 for 90° ≤ y ≤ 180°, we can calculate cos^2(y) as follows:
cos^2(y) = (-4/5)^2 = 16/25
Now we substitute this value back into the double-angle identity:
cos(2y) = 2(16/25) - 1
= 32/25 - 1
To simplify the expression, we first need to find a common denominator:
cos(2y) = 32/25 - 25/25
= (32 - 25)/25
= 7/25
Therefore, the value of cos 2y is 7/25.