Question

Exact values of reference angles?
sin 9pi/4
tan 19pi/4
sec -3pi/4

Answer 1

Reference angle is the angle closest to the x-axis.

Answer 2

well you need to decide which quadrant you're in

\[2\pi = 1 \times revolution\]

so \[\sin(\frac{9\pi}{4}) = \sin(2\pi + \frac{\pi}{4}) = \sin(\frac{\pi}{4})\]

which is an exact value


\[\tan(\frac{19\pi}{4}) = \tan(4\pi + \frac{3\pi}{4}) = \tan(\frac{3\pi}{4})\]

which is an exact value in the 2nd quadrant where tan is negative

the last 1 you move backwards by the angle... so its 3rd quadrant...

where sec is negative

hope it helps

Answer 3

At the x-axis, the radians there are:

Answer 4

Thanks both of you, that really helped!