Free preview

7.3 Double-Angle, Half-Angle, and Product-Sum Formulas

Focus on double-angle sine and half angle sign.

Before you solve

Ideas in this lesson

Explore the lesson brief and the worked example for Idea $1$ . Create a free account to continue with the remaining ideas and practice.

01Double-angle formulasWorked steps · five questions 02Power-reducing formulasWorked steps · five questions 03Half-angle formulasWorked steps · five questions 04Product-to-sum and sum-to-productWorked steps · five questions

Lesson brief and rules

7.3 Double-Angle, Half-Angle, and Product-Sum Formulas

$\sin (2\theta )=2\sin \theta \cos \theta$ .

Worked example

1

01 / If

\sin \theta =\dfrac{9}{15}

and

\cos \theta =\dfrac{12}{15}

, find

\sin (2\theta )

02 /

2\sin \theta \cos \theta =2(\dfrac{3}{5})(\dfrac{4}{5})=\dfrac{24}{25}

(

Set

4

)

03 / Answer:

\dfrac{24}{25}

Worked example 2 · Half angle sign

For $0<\theta <\pi$ , what sign is $\sin (\dfrac{\theta }{2})$ ?

$\dfrac{\theta }{2}$ lies in Quadrant I, where sine is positive. Answer: Positive

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

MathLab with Mr. Ahmed

7.3 Double-Angle, Half-Angle, and Product-Sum Formulas

Ideas in this lesson

7.3 Double-Angle, Half-Angle, and Product-Sum Formulas