Question

Suppose that θ is an angle with Sin(θ) = 3/4 and angle θ is in the second quadrant. Find Sin(2θ).

A. 3/8
B. 1/8
C. -3/8
D. -1/8

Answer 1

To find Sin(2θ), use the double angle formula for sine and take into account the given value of Sin(θ) and the quadrant of θ. The value of Sin(2θ) is approximately -0.53.

Step-by-step explanation:

To find Sin(2θ), we can use the double angle formula for sine:

Sin(2θ) = 2 * Sin(θ) * Cos(θ)

Given that Sin(θ) = 3/4 and θ is in the second quadrant, we can determine that Cos(θ) is negative. Using the Pythagorean identity, we can find the value of Cos(θ) = -√(1 - Sin^2(θ)) = -√(1 - (3/4)^2) = -√(1 - 9/16) = -√(7/16) = -√7/4.

Plugging these values into the double angle formula, we get:

Sin(2θ) = 2 * (3/4) * (-√7/4) = -3√7/8 = -0.53

Therefore, the correct answer is C. -3/8.