Question

What is sin2α if sin α=0.9 and π/2≺α≺π

Answer 1

Given,

sin∅ = 0.9 = 9/10

From the relation sin²∅ + cos²∅ = 1,

cos²∅ = 1 - sin²∅

cos²∅ = 1 - (9/10)²

cos²∅ = 19/100

cos∅ = ± √19/10

Since π/2 < ∅ < π, cos∅ is negative

cos∅ = - √19/10

Now,

sin2∅ = 2sin∅cos∅

sin2∅ = 2(9/10)(- √19/10)

sin2∅ = 2 × (-9√9)/100

sin2∅ = - 9√9/50

Answer 2

Answer:

The value of sin 2α is 0.785.

Step-by-step explanation:

It is provided that sin α = 0.90.

The formula of sin 2α is,

sin 2α = 2 sin α cos α

Compute the value of sin 2α as follows:

$sin 2\alpha =2sin\alpha cos\alpha \\=2sin\alpha \sqrt{1-sin^{2}\alpha }\\=2\times0.90\times\sqrt{1-0.90^{2}}\\=2\times0.90\times0.4359\\=0.78462\\\approx0.785$

Thus, the value of sin 2α is 0.785.