Use reference angles to find the exact value of cos(-17pi/6)
To find the exact value of cos(-17pi/6), we can use the reference angle and apply the cosine function to determine the value in the specified interval.
Step 1: Determine the reference angle.
The reference angle is the acute angle formed between the terminal side of the angle and the x-axis.
In this case, the angle -17pi/6 is in the fourth quadrant where the cosine function is positive. To find the reference angle, we can count backward from 2pi (360 degrees) to -17pi/6.
2pi - 17pi/6 = 12pi/6 - 17pi/6 = -5pi/6.
So, the reference angle is 5pi/6.
Step 2: Determine the sign.
In quadrant IV, where -17pi/6 lies, the cosine function is positive.
Step 3: Determine the exact value.
Since the reference angle is 5pi/6 and the cosine function is positive in the fourth quadrant, we can use the reference angle to find cos(-17pi/6).
cos(-17pi/6) = cos(5pi/6) = cos(π - 5pi/6) = -cos(5pi/6).
To evaluate -cos(5pi/6), we can use the values on the unit circle. On the unit circle, the value of cos(5pi/6) is -√3/2.
So, the exact value of cos(-17pi/6) is -(-√3/2) = √3/2.