Question

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GIVEN THAT TAN Ꝋ= - 4/3 AND Ꝋ IS IN QUADRANT II, FIND SIN 2Ꝋ

Answer 1

sin 2θ = -24/25

Explanation:

see the below formula of sin x in terms of tan x

by substituting => -4/3 / ± √(16/9 + 1)

=> -4/3 / ± √(25/9)

=> -4/3 / ± 5/3

=> ± -4/5

=> ± 4/5

as theta is in second quadrant is in 2nd quadrant sin value is positive

so sin θ = 4/5 and cos θ = -3/5

now sin 2θ = 2 sinθcosθ

= 2 * 4/5 * -3/5

= -24/25