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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7.2 Addition and Subtraction Formulas

Focus on sine addition and sine sum.

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.

01Exact values with addition and subtraction formulasWorked steps · five questions02Recognizing and using the formulas in reverseWorked steps · five questions03Values of sin(s + t) from given informationWorked steps · five questions04Cofunction identities and proofs with sumsWorked steps · five questions
Lesson brief and rules

7.2 Addition and Subtraction Formulas

sin⁡(A+B)=sin⁡\sin (A+B)=\sin A cos⁡B+cos⁡\cos B+\cos A sin⁡B\sin B.

Worked example 11
01 / Compute sin⁡(30∘+60∘+1080∘)\sin (30^{\circ}+60^{\circ}+1080^{\circ}) using the addition formula.
02 / sin⁡30∘cos⁡60∘+cos⁡30∘sin⁡60∘=14+34=1\sin 30^{\circ}\cos 60^{\circ}+\cos 30^{\circ}\sin 60^{\circ}=\dfrac{1}{4}+\dfrac{3}{4}=1. (( Set 44.))
03 / Answer: 11
Worked example 2 · Sine sum

Evaluate sin⁡(30∘+60∘)\sin (30^{\circ}+60^{\circ}).

Sine addition gives sin⁡30∘cos⁡60∘+cos⁡30∘sin⁡60∘=1\sin 30^{\circ}\cos 60^{\circ}+\cos 30^{\circ}\sin 60^{\circ}=1. 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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