In this worksheet, you will work with trigonometric functions of any angle using the ASTC circle to determine in which quadrants the functions are positive, before finding "equivalent" trig ratios of angles less than 90º.
Remember that angles are measured anticlockwise from the 0º line.
The following diagram shows the angle 200º on the ASTC circle.
Notice that the 200º line makes an angle of 20º with the horizontal.
We always look at the horizontal.
This shows that:
tan 200º = tan 20º as tan is positive in this 3rd quadrant.
sin 200º = - sin 20º as sin is negative in this 3rd quadrant.
cos 200º = -cos 20º as cos is negative in this 3rd quadrant.
Select the trigonometric functions which are equal to one another.
sin 165º, -sin 65º, sin 15º, sin 525º, -sin 15º
On the ASTC circle, both 165º and 525º make an angle of 15º with the horizontal.
The only trig ratio that is positive in this quadrant is sin.
sin 525º = sin 165º = sin 15º