Trig Equations with Identities
Use identities to factor trig equations.
Key idea
Use identities to factor trig equations.
In depth
When an equation mixes functions or angles, rewrite using identities so there is a single function, then factor or solve as a quadratic. Never divide by a trig expression that might be zero.
Worked example
2sin²x + sin x − 1 = 0 → (2sin x − 1)(sin x + 1) = 0 → sin x = 1/2 or −1.
Real-world uses
- Solving oscillation and wave problems in physics and engineering
Common mistake
Dividing both sides by sin x, losing solutions where sin x = 0.
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 Trig Equations with Identities?
Use identities to factor trig equations. It is a topic at the expert level in Trigonometry.
Where is Trig Equations with Identities used in real life?
Real-world examples: Solving oscillation and wave problems in physics and engineering.
What should I learn before Trig Equations with Identities?
Make sure you are comfortable with Basic Trig Equations, the previous topic in Trigonometry.
What is a common mistake with Trig Equations with Identities?
Dividing both sides by sin x, losing solutions where sin x = 0.
How can I practise Trig Equations with 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 Trig Equations with Identities?
Move on to Law of Sines next.
Related expert topics in Trigonometry
- Half Angle Formulas – Trig of θ/2.
- Power Reducing Formulas – Reduce squares to first powers of cos 2θ.
- Product-to-Sum Formulas – Convert products into sums.
- Sum-to-Product Formulas – Convert sums into products.
- Triple Angle Formulas – sin3θ and cos3θ in terms of θ.
- Trig and Inverse Trig Compositions – Evaluate expressions like sin(arccos x).