Question

If the measure of angle θ is 11 ⁢ π 6 , which statements are true? cos ( θ ) = 3 2 sin ( θ ) = 1 2 the measure of the reference angle is 45 ∘ . tan ( θ ) = 1 the measure of the reference angle is 60 ∘ . the measure of the reference angle is 30 ∘ .

Answer 1

The measure of angle θ is 11π/6. The statement 'sin(θ) = 1/2' is true.

Step-by-step explanation:

The measure of angle θ is 11π/6.

Statement 1: cos(θ) = 3/2

To determine if this statement is true, we can use the unit circle. Since θ is in the third quadrant, the cosine value is negative. Therefore, cos(θ) = -1/2, not 3/2. So, statement 1 is FALSE.

Statement 2: sin(θ) = 1/2

To determine if this statement is true, we can use the unit circle. Since θ is in the third quadrant, the sine value is positive. Therefore, sin(θ) = 1/2. So, statement 2 is TRUE.

Statement 3: tan(θ) = 1

Since tan(θ) = sin(θ)/cos(θ), we can substitute the values we found earlier to get tan(θ) = (1/2)/(-1/2) = -1. So, statement 3 is FALSE.

From the unit circle, we can see that the reference angle for θ is π/6 radians or 30 degrees. Therefore, statement 4 is FALSE. The correct answer is statement 2 is TRUE.