Cofunction Identities
Sine of an angle equals cosine of its complement.
Key idea
Sine of an angle equals cosine of its complement.
In depth
sin(90° − θ) = cos θ, cos(90° − θ) = sin θ, tan(90° − θ) = cot θ. Complementary angles in a right triangle swap opposite and adjacent sides, so the functions swap.
Worked example
sin 20° = cos 70°.
Formula
Real-world uses
- Switching between angles in surveying and drafting
- Connecting sine and cosine of complementary angles
Common mistake
Using 180° − θ instead of 90° − θ.
How to learn this
- Read the key idea and say it in your own words.
- Work through the worked example, then try a similar problem.
- Use the interactive lesson’s visual and mini-quiz to check the pattern.
Frequently asked questions
What is Cofunction Identities?
Sine of an angle equals cosine of its complement. It is a topic at the advanced level in Trigonometry.
What is the formula for Cofunction Identities?
The key formula is sin(90°−θ) = cosθ.
Where is Cofunction Identities used in real life?
Real-world examples: Switching between angles in surveying and drafting; Connecting sine and cosine of complementary angles.
What should I learn before Cofunction Identities?
Make sure you are comfortable with Quotient Identities, the previous topic in Trigonometry.
What is a common mistake with Cofunction Identities?
Using 180° − θ instead of 90° − θ.
How can I practise Cofunction Identities?
Open the interactive lesson, play with the visual, then answer the three-question mini-quiz. Getting two right marks the topic complete.
What comes after Cofunction Identities?
Move on to Even-Odd Identities next.
Related advanced topics in Trigonometry
- Graph of Tangent – Periodic with vertical asymptotes at odd multiples of π/2.
- Phase Shift – Horizontal translation of a wave.
- Vertical Shift and Midline – Moves the wave up or down.
- General Sinusoid – Combine amplitude, period, phase and shift.
- Graphs of Reciprocal Trig Functions – Secant, cosecant and cotangent graphs.
- Pythagorean Identity – The key identity from the unit circle.