Recover a Squared Trigonometric Value
Unit-circle coordinates satisfy x²+y²=1, giving cos²θ+sin²θ=1.
About 25 minutes, plus any extended practice
Open lesson 1Precalculus: Trigonometric Identities and Equations
An identity holds for all inputs in its domain, while an equation asks for particular angle solutions. Algebraic identities, angle formulas and geometric laws must retain signs, intervals and their defining conditions.
Before you begin
- Use unit-circle values; solve equations involving squares; distinguish degrees from radians.
Choose by skill rather than age alone. Read with an adult when useful, revisit a lesson, or explore another grade.
Follow the lesson sequence
Use the Double-Angle Sine Identity
Sine of twice an angle equals twice the product of its sine and cosine.
About 25 minutes, plus any extended practice
Open lesson 2Find Every Solution in a Stated Cycle
A positive sine level can occur twice in a full cycle, once on each side of its maximum.
About 25 minutes, plus any extended practice
Open lesson 3Use an Included Angle in a Nonright Triangle
The law of cosines generalizes the right-triangle relationship by subtracting twice the side product times the included-angle cosine.
About 25 minutes, plus any extended practice
Open lesson 4Review and transfer
After the lessons, try 4 new review cases and a practical task. Each answer has an explanation and a link back to the related lesson.
Open the unit reviewGuest answers are temporary. Keep your own paper or document; this unit does not certify completion or record a school grade.
Topic references
- OpenStax mathematical topic reference: topic reference — Precalculus: Trigonometric Identities and Equations
These references informed the topic selection. They do not certify complete standards alignment.