Evaluate each value as a trigonometric function of an angle in Quadrant 1.
#1 cos (27pi/8)
27 pi/8 = 3 pi + 3 pi/8
that is 180 degrees + 67.5 degrees
that is in quadrant 3 where cos is negative
so
-cos 3 pi/8 radians
or
-cos 67.5 degrees
To evaluate the value of the trigonometric function cos(27π/8) in Quadrant 1, we need to find the reference angle in Quadrant 1 that has the same cosine value as cos(27π/8).
The reference angle is the acute angle formed between the terminal side of the angle and the x-axis. In Quadrant 1, the cosine function is positive, so we can focus on finding the positive cosine value that is equivalent to cos(27π/8).
Here's how you can find the reference angle in Quadrant 1:
1. Start by converting 27π/8 to degrees. We know that π radians is equivalent to 180 degrees, so we can use the formula:
degrees = radians * (180/π)
degrees = (27π/8) * (180/π)
= (27*180)/(8)
= 405/8 degrees
2. Now we have the angle in degrees, which is 405/8 degrees. In Quadrant 1, the reference angle with the same cosine value is the angle formed between the x-axis and the terminal side of the angle.
3. Since we are working in Quadrant 1, the reference angle is the angle formed by rotating clockwise from the positive x-axis. To find this angle, we subtract the angle in degrees from 360:
reference angle = 360 - (405/8) degrees
We can simplify this further if needed.
After finding the reference angle, you can evaluate the cosine function of the reference angle using a scientific calculator or trigonometric table.