Trig Ratios

If you are unsure on the concept of trig ratios, please go to trig ratios. In this course, we will be continue working on more examples of trig ratios. Later, you would have a chance to work on trig ratios.

Note that if you are unclear on the diagrams on trig ratios or basic angles , you can remind yourself at trig ratio.

Examples

b) Find the simplified trig ratio of cosine .

For this question, we have to realize that is in radians.

is in the 3 rd quadrant and the basic angle of is . The basic angle is measured as the acute angle which OP makes with the x-axis. Since cosine is negative in the 3 rd quadrant as seen in the ‘ASTC' diagram,

c) cosine

There's a slight different twist to this question. Try drawing out the diagram before proceeding with finding the trig ratios.

is in the 3 rd quadrant and the basic angle

is ( ) . As seen in the ‘ASTC' diagram, cosine is negative in the 3 rd quadrant. As a result, the trig ratio is . We can further simplify this trig ratio to -sine through the use of complementary angles .

Scholar's tips: Supplementary angles and complementary angles can be derived from using the above steps in determining trigonometry ratios.

'Try it Out Yourself' Section

Simplify the following trig ratios.

a)

b)