For each angle θ listed below, find the reference angle α, and then find sin θ. Round sin θ to four decimal places, if necessary.
θ = -30° ? ?
The reference angle for -30° can be found by taking the absolute value of the angle and finding the acute angle between 0 and 360 degrees. In this case, the acute angle between 0 and 360 degrees is 30 degrees. So the reference angle α is 30°.
To find sin θ, we can use the relationship between sine and reference angle. Since the sin function is positive in the second quadrant, sin θ is equal to sin α.
sin θ = sin α = sin 30°
Using a calculator, we find that sin 30° is approximately 0.5000.
So sin θ ≈ 0.5000
To find the reference angle α for θ = -30°, we need to find the positive angle that is closest to the x-axis and that has the same trigonometric values.
Since -30° is in the fourth quadrant, we can find the reference angle by adding 360° to -30°:
α = -30° + 360° = 330°
The sine of θ can be found by converting the reference angle α to radians and taking the sine:
sin θ = sin α = sin 330° ≈ -0.5
So, sin θ is approximately -0.5 rounded to four decimal places.