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.
If cos 15º = 0.966, calculate
On the ASTC circle, 525º makes an angle of 15º with the horizontal.
The only trig ratio that is positive in this quadrant is sin, which means that cos is negative in this quadrant.
cos 525º = cos 165º = - cos 15º = -0.966