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Nat2105 [25]
3 years ago
6

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

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

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

Now recall the double angle identity for sine:

sin(2<em>θ</em>) = 2 sin(<em>θ</em>) cos(<em>θ</em>)

==>   sin(2<em>θ</em>) = 2 (-3/5) (4/5) = -24/25

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