Question

What is the reference angle for θ = 210◦ ? Using that reference angle, determine the vaules for the six trigonometric functions of 210◦.

Answer 1

Reference angle is `30^@`, angle is in QIII

`sin210^@=-1/2`, `csc210^@=-2`

`cos210^@=-sqrt(3)/2`, `sec210^@=-(2sqrt(3))/3`

`tan210^@=sqrt(3)/3`, `cot210^@=sqrt(3)`

Explanation:

The reference angle is found by calculating the difference between `theta` and the x-axis. In this problem, 210 is closest to 180, so `210^@-180^@=30^@`. This is your reference angle. We can calculate the values of all six trig ratios using a combination of the reference angle and the quadrant in which it lies (Q3). In Q3, both `sintheta` and `costheta` are negative. But `tantheta` is positive. Armed with all this information, we can get the values of the six trig ratios above.