The reference angle for (5pi)/4 is pi/4 , which has a terminal point of (sqrt2/2), (sqrt2/2). What is the terminal point of 5pi/4?

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Using the unit circle, it is found that the terminal point of the angle 5pi/4 is given by:

A. ?f=%5Cleft( %5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%2C%20 %5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5Cright)

What is the unit circle?

For an angle ?f=%5Ctheta the unit circle is a circle with radius 1 containing the following set of points: ?f=(%5Ccos%7B%5Ctheta%7D%2C%20%5Csin%7B%5Ctheta%7D).

The angle 5pi/4 is in the third quadrant, as it is greater than pi and less than 1.5pi, in which both the sine and the cosine are negative. Hence, considering the reference angle, we have that:

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?f=(%5Ccos%7B(%5Cleft(%5Cfrac%7B5%5Cpi%7D%7B4%7D%5Cright)%7D%2C%20%5Csin%7B(%5Cleft(%5Cfrac%7B5%5Cpi%7D%7B4%7D%5Cright)%7D)%20%3D%20( %5Ccos%7B(%5Cleft(%5Cfrac%7B%5Cpi%7D%7B4%7D%5Cright)%7D%2C%20 %5Csin%7B(%5Cleft(%5Cfrac%7B%5Cpi%7D%7B4%7D%5Cright)%7D)%20%3D%20%5Cleft( %5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%2C%20 %5Cfrac%7B%5Csqrt%7B2%7D%7D%7B2%7D%5Cright)

Hence option A is correct.


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