I just want to know if this answer is correct, 120/169.
Use identities to find the indicated value for each angle measure.
sin θ = 12/13, cos θ > 0
Find cos (2θ).
You know it will be in quadrant 2 where cos is negative
cos^2-sin^2 = 25/169 - 144/169 = -119/169
Cos0= -3/5 where pie over 2 _<0 < pie
Fin tan 20 could you explain how to get the answer?
To find the value of cos (2θ), we can use the double angle formula for cosine. The double angle formula states that cos (2θ) = 2 * cos^2(θ) - 1.
Given that sin θ = 12/13 and cos θ > 0, we can find cos θ using the Pythagorean identity: sin^2(θ) + cos^2(θ) = 1. Plugging in the value of sin θ, we get:
(12/13)^2 + cos^2(θ) = 1
144/169 + cos^2(θ) = 1
cos^2(θ) = 1 - 144/169
cos^2(θ) = 25/169
Since cos θ is positive, we know that cos θ > 0. Taking the square root of both sides of the equation, we get:
cos θ = √(25/169)
cos θ = 5/13
Now we can substitute the value of cos θ into the double angle formula:
cos (2θ) = 2 * cos^2(θ) - 1
cos (2θ) = 2 * (5/13)^2 - 1
cos (2θ) = 2 * 25/169 - 1
cos (2θ) = 50/169 - 1
cos (2θ) = (50 - 169)/169
cos (2θ) = -119/169
Therefore, the value of cos (2θ) is -119/169.