MathLab with Mr. Ahmed

MathLab with Mr. Ahmed is a math learning website by Ahmed Amasha, a mathematics teacher teaching the American curriculum. Explore Algebra 2, Precalculus, Calculus, and SAT and PSAT Math Prep through lessons, focused practice and printable resources.

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7.1 Trigonometric Identities

Focus on pythagorean identity and reciprocal identity.

Before you solve

Ideas in this lesson

Explore the lesson brief and the worked example for Idea 11. Create a free account to continue with the remaining ideas and practice.

01Writing expressions in terms of sine and cosineWorked steps · five questions02Simplifying with the Pythagorean identitiesWorked steps · five questions03Proving identitiesWorked steps · five questions04Trigonometric substitutionWorked steps · five questions
Lesson brief and rules

7.1 Trigonometric Identities

sin⁡2θ+cos⁡2θ=1\sin ^{2}\theta +\cos ^{2}\theta =1; divide by cos⁡2θ\cos ^{2}\theta only where cos⁡θ≠0\cos \theta \ne 0.

Worked example 11
01 / If sin⁡2θ=38\sin ^{2}\theta =\dfrac{3}{8}, find cos⁡2θ\cos ^{2}\theta .
02 / cos⁡2θ=1−sin⁡2θ=8−38\cos ^{2}\theta =1-\sin ^{2}\theta =\dfrac{8-3}{8}.
03 / Answer: 58\dfrac{5}{8}
Worked example 2 · Reciprocal identity

Simplify sin⁡θ⋅csc⁡θ\sin \theta \cdot \csc \theta where defined.

csc⁡θ=1sin⁡θ\csc \theta =\dfrac{1}{\sin \theta } when sin⁡θ≠0\sin \theta \ne 0. Answer: 11

15 questions covering every idea, with a worked answer for each.Start practice ↗
Textbook reference: Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, 7th ed. (Cengage, 2016). The explanations and practice here are original, organized by textbook section.

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