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.

MathLabwith Mr. Ahmed
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7.5 More Trigonometric Equations

Focus on squared trig equation and square-root branches.

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.

01Equations using identitiesWorked steps · five questions02Equations with multiple anglesWorked steps · five questions03Equations needing a calculatorWorked steps · five questions
Lesson brief and rules

7.5 More Trigonometric Equations

Use identities or substitution and verify all roots in the specified interval.

Worked example 11
01 / Solve sin⁡2(3θ)=1\sin ^{2}(3\theta )=1 on [0,2π3)[0,\dfrac{2\pi }{3}).
02 / sin⁡(3θ)=±1\sin (3\theta )=\pm 1 when 3θ=π23\theta =\dfrac{\pi }{2} or 3π2\dfrac{3\pi }{2} in the interval; divide both angles by 33.
03 / Answer: π6,π2\dfrac{\pi }{6}, \dfrac{\pi }{2}
Worked example 2 · Square-root branches

Solve sin⁡2θ=1\sin ^{2}\theta =1 on [0,2π)[0,2\pi ).

sin⁡θ=±1\sin \theta =\pm 1, producing both solutions. Answer: π2,3π2\dfrac{\pi }{2}, \dfrac{3\pi }{2}

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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