find the reference angle of -11pi/3
David, really now !
After getting help for so many trig question, don't you think it is time that you try some of these yourself?
Especially the rather simple ones, like your last two?
Let us know what you get and we'll check them
To find the reference angle of a given angle, follow these steps:
Step 1: Determine the principal angle
- The principal angle is the positive equivalent of the given angle within one full revolution (360 degrees) or 2π radians.
- To find the principal angle, add or subtract (if necessary) a complete revolution (or 2π radians) until you obtain a positive angle.
For the given angle -11π/3:
- Start with -11π/3
- To make it positive, add 6π (2π x 3) to get -11π/3 + 6π = -11π/3 + 18π/3 = 7π/3
Step 2: Find the reference angle
- The reference angle is the acute (positive) angle formed between the terminal side of the given angle and the x-axis.
For the principal angle 7π/3:
- Draw the angle in standard position, starting from the positive x-axis and rotating counter-clockwise.
- The angle 7π/3 is between the negative x-axis and the terminal side.
To find the reference angle:
- Subtract the principal angle from π radians (180 degrees) or π/2 radians (90 degrees) to get the reference angle.
- π - 7π/3 = 3π/3 - 7π/3 = -4π/3
However, for reference angles, we only consider the positive value.
- Take the absolute value of -4π/3 to get the positive reference angle: |-4π/3| = 4π/3
Therefore, the reference angle of -11π/3 is 4π/3.