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
Free preview

7.4 Basic Trigonometric Equations

Focus on sine equation and unit circle sine solution.

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.

01Solving basic trig equationsWorked steps · five questions02Solving by isolating the trig functionWorked steps · five questions03Solving by factoringWorked steps · five questions
Lesson brief and rules

7.4 Basic Trigonometric Equations

Solve within the stated interval; sin⁡θ=0\sin \theta =0 at integer multiples of π\pi .

Worked example 11
01 / Solve sin⁡(3θ)=0\sin (3\theta )=0 on [0,2π3)[0,\dfrac{2\pi }{3}).
02 / The zeros of sin⁡(3θ)\sin (3\theta ) occur at 3θ=0,π3\theta =0,\pi in this interval, so θ=0,π3\theta =0,\dfrac{\pi }{3}.
03 / Answer: 0,π30, \dfrac{\pi }{3}
Worked example 2 · Unit circle sine solution

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

The unit circle has y=1y=1 at π2\dfrac{\pi }{2}. Answer: π2\dfrac{\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.

Read this lesson preview