What is the reference angle for θ = -195 degrees? Is it 75 degrees?
A reference angle is the positive acute angle between an angle and the horizontal axis.
For the different possible cases, see:
http://www.mathwarehouse.com/trigonometry/reference-angle/finding-reference-angle.php
So is it 15 degrees?
that is correct.
To determine the reference angle for an angle in degrees, you can follow these steps:
1. Consider the given angle, θ = -195 degrees. Since the angle is negative, we can interpret it as starting from the negative x-axis and rotating clockwise.
2. To find the reference angle, we need to identify the corresponding positive acute angle in the counterclockwise direction from the x-axis.
3. To do this, add 360 degrees to the given negative angle (-195 degrees + 360 degrees = 165 degrees). This ensures that the resulting angle remains in the same position but becomes positive.
4. Now, observe the resulting angle, which is 165 degrees. The reference angle is the positive acute angle formed between the x-axis and the terminal side of this angle.
5. In this case, the reference angle is 15 degrees (165 degrees - 150 degrees).
Therefore, the reference angle for θ = -195 degrees is 15 degrees, not 75 degrees as initially suggested.