Example 1:

Find the value of cos2pi/3

Solution:
Since 2pi/3 is in quadrant II, we know the sign of cos2pi/3 is negative. Also the reference number for 2pi/3 is pi/3. Therefore we get:
cos2pi/3 = -cospi/3 = -1/2



Example 2:

Find the value of tan(-pi/3)

Solution:
The reference number for -pi/3 is pi/3 and we know from the diagram (before this set of exercises) that -pi/3 is in quadrant IV. Therefore, tan(-pi/3) is negative. Thus:
tan(-pi/3) = -tan(pi) = -SQRT(3)



Example 3:

Find the value of sin19pi/4.

Solution:
We know that 19pi/4 is coterminal with 3pi/4. The reference number for 3pi/4 is pi/4.
Sin(3pi/4) is positive since 3pi/4 is in the second quadrant. Hence we get:
sin19pi/4 = Sin3pi/4 = +sinpi/4 = SQRT(2)/2

Return to the tutorial