Complementary Angles


Complementary angles are angles that add up to 90 . In this course, we shall look at how complementary angles are derived and make it easier for you to learn about them in class. For complementary angles, the trigonometry function changes when it is simplified.

Sine Cosine

Tangent Cotangent

Secant Cosecant

This means that the sine function will change to a cosine function. Tangent and secant functions will change accordingly as seen above. The purpose of the complementary angles equation is to reduce it to a trigonometry function with only ? in it. Let's take sine as an example.

1) Like supplementary angles, we look at the quadrant at which lies in . It's in the 3rd quadrant

2) By looking at the ‘ASTC' diagram (check it at trig ratio ) , we determine the sign (+ve or –ve ) for that particular trigonometry function at that angle. In this case, it's negative.

3) Thus we would be able to deduce sine = - cosine by switching to its corresponding trigonometry function and adding the negative sign.

Other complementary angles can be found in this manner. As such , if you fail to memorise them in exams, you can choose to derive it on the spot. However, we have also put up a list of complementary angles for your convenience.

List of Complementary Angles

sine = cosine

sine angle that shows the complementary angles = cosine

sine = - cosine

sine = - cosine

secant = cosecant

secant = -cosecant

secant = - cosecant

secant = cosecant

tangent  angle to show complementary angles = cotangent

tangent = - cotangent

tangent = cotangent simplified version of complementary angles

tangent = - cotangent

Remember that these formulas would also hold for cosine ,cotangent and cosecant. Replace the above complementary angle formulas with their respective related trigonometry functions and you would get the complementary angles for those terms.

For instance , cotangent = tangent simplified version of complementary angles.

Try applying these concepts in our examples of trigonometry identities.

You may wish to consider exploring supplementary angles as well.

Return to Trigonometry Help or Basic Trigonometry .