Suppose Tangent (x) = StartFraction 7 Over 2 EndFraction where 180° < x < 270°. What is the value of sin(2x)?

Step-by-step explanation:

Given Tanx = 7/2

Since tanx = opp/adj

Opposite = 7

Adjacent = 2

Hyp = √7²+2²

hyp = √53

cos x = adj/hyp

cosx = 2/√53

sinx = opp/hyp

sinx = 7/√53

Sin(2x) = sinxcosx + cosx sinx

sin(2x) = 2sin(x)cos(x)

Substitute

sin2x = 2(7/√53)(2/√53)

sin(2x) = 28/53

Hence the value of sin(2x) is 28/53

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