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

1 Answer
Mar 1, 2018

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

sin210^@=-1/2sin210=12, csc210^@=-2csc210=2

cos210^@=-sqrt(3)/2cos210=32, sec210^@=-(2sqrt(3))/3sec210=233

tan210^@=sqrt(3)/3tan210=33, cot210^@=sqrt(3)cot210=3

Explanation:

The reference angle is found by calculating the difference between thetaθ and the x-axis. In this problem, 210 is closest to 180, so 210^@-180^@=30^@210180=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 sinthetasinθ and costhetacosθ are negative. But tanthetatanθ is positive. Armed with all this information, we can get the values of the six trig ratios above.