Use a double angle or half angle identity to find the exact value of each expression

Mathematics

1 answer:

inna [77]3 years ago

4 0

θ is given to be in the fourth quadrant (270° < θ < 360°) for which sin(θ) < 0 and cos(θ) > 0. This means

cos²(θ) + sin²(θ) = 1 ==> sin(θ) = -√[1 - cos²(θ)] = -3/5

Now recall the double angle identity for sine:

sin(2θ) = 2 sin(θ) cos(θ)

==> sin(2θ) = 2 (-3/5) (4/5) = -24/25

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