Quotient Identities
Tangent and cotangent in terms of sine and cosine.
Key idea
Tangent and cotangent in terms of sine and cosine.
In depth
tan θ = sin θ / cos θ and cot θ = cos θ / sin θ. They show tangent as slope on the unit circle and allow rewriting expressions only in sin and cos.
Worked example
sin θ = 3/5, cos θ = 4/5 → tan θ = 3/4.
Formula
Real-world uses
- Rewriting expressions in terms of sine and cosine when solving physics problems
Common mistake
Dividing in the wrong order.
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 Quotient Identities?
Tangent and cotangent in terms of sine and cosine. It is a topic at the advanced level in Trigonometry.
What is the formula for Quotient Identities?
The key formula is tanθ = sinθ/cosθ.
Where is Quotient Identities used in real life?
Real-world examples: Rewriting expressions in terms of sine and cosine when solving physics problems.
What should I learn before Quotient Identities?
Make sure you are comfortable with Other Pythagorean Identities, the previous topic in Trigonometry.
What is a common mistake with Quotient Identities?
Dividing in the wrong order.
How can I practise Quotient 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 Quotient Identities?
Move on to Cofunction 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.