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.
Change the following to equivalent trigonometric functions of angles less than 90º:
sin 165º, cos 165º and tan 165º
Draw 165º on the ASTC circle and then put in the angle that it makes with the horizontal.
The only trig ratio that is positive in this quadrant is sin 165º.
sin 165º = sin 15º as sin is positive in this 2nd quadrant.
cos 165º = - cos 15º as cos is negative in this 2nd quadrant.
tan 165º = - tan 15º as tan is negative in this 2nd quadrant.