Supplementary Angles

Concept

Supplementary angles are angles that add up to 180 . We are going to look at how supplementary angles are applied in trigonometry. The purpose of the supplementary angles equations is to reduce it to a trigonometry function with only in it. For instance, sine = - sine . It can be clearly seen that the trigonometry function (sine) does not change. Let us look at how we derived the supplementary angles.

1) Look at the quadrant at which the lies in. It's in the 3rd quadrant .

2) Then find the sign ( +ve or -ve ) of the sine in the 'ASTC' diagram ( Check it at trig ratio). It is negative.

3) So, we can easily obtain that = - sin by adding the negative sign.

Other supplementary angles can similarly be found in this manner. As such , it is not necessary to memorise the supplementary angle formulas by heart. Nevertheless ,we have provided a list of supplementary angles for your convenience.

List of Supplementary Angles

sine = sine

sine = - sine

sine supplementary angles = - sine

tangent = - tangent

tangent trig identities for supplementary angles = tangent

tangent = - tangent

cosine picture showing the supplementary angle = - cosine

cosine = - cosine

cosine = cosine

Trigonometry functions like secant and cosecant are related to the cosine and sine function. Thus they follow the same rules. For instance, by looking at the supplementary angles for cosine, we can tell that secant = -secant . This is the same for cosecant and cotangent which have relations with sine and tangent respectively.

Look at how you can apply this concept in examples of proving trigonometry identities.

You may wish to consider taking a look at complementary angles as well.

Return to Trigonometry Help or Basic Trigonometry .