Question

If sin(θ) = 4/3, what is sin(2θ)?

Option 1: sin(2θ) = 24/9
Option 2: sin(2θ) = 7/5
Option 3: sin(2θ) = 8/5
Option 4: sin(2θ) = 16/9

Answer 1

The value of sin(2θ) is undefined.

Step-by-step explanation:

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

sin(2θ) = 2sin(θ)cos(θ)

Given that sin(θ) = 4/3, we can substitute this value into the formula:

sin(2θ) = 2(4/3)cos(θ)

To find the value of cos(θ), we can use the pythagorean identity:

cos²(θ) = 1 - sin²(θ)

cos²(θ) = 1 - (4/3)²

cos²(θ) = 1 - 16/9

cos²(θ) = 9/9 - 16/9

cos²(θ) = -7/9

Since cos²(θ) is negative, we know that cos(θ) is undefined.

Therefore, sin(2θ) is also undefined.