HSF.TF.C.9: Prove angle sum formulas — Practice

Work through problems with immediate feedback

Concepts

Which of the following is the correct formula for $\sin(A + B)$ ?

$\sin(A + B) = \sin A + \sin B$

$\sin(A + B) = \sin A \cos B + \cos A \sin B$

$\sin(A + B) = \sin A \cos B - \cos A \sin B$

$\sin(A + B) = \cos A \cos B - \sin A \sin B$

Which formula correctly gives $\cos(A + B)$ ?

$\cos(A + B) = \cos A \cos B + \sin A \sin B$

$\cos(A + B) = \cos A \cos B - \sin A \sin B$

$\cos(A + B) = \cos A + \cos B$

$\cos(A + B) = \sin A \cos B + \cos A \sin B$

The double angle formula $\sin(2A) = 2\sin A \cos A$ is best described as:

A completely new identity that must be memorized independently

The addition formula for $\sin(A + B)$ with $B$ replaced by $A$

A consequence of the Pythagorean identity only

A definition of $\sin(2A)$ with no connection to $\sin(A + B)$

What is the correct formula for $\tan(A + B)$ ?

$\tan(A + B) = \tan A + \tan B$

$\tan(A + B) = \dfrac{\tan A - \tan B}{1 + \tan A \tan B}$

$\tan(A + B) = \dfrac{\tan A + \tan B}{1 - \tan A \tan B}$

$\tan(A + B) = \tan A \cdot \tan B$

Complete the subtraction formula for sine by filling in the blank:

$\sin(A - B) = \sin A \cos B$ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ ̲ $\cos A \sin B$

sign between the two cross-product terms:

Procedures

Using the angle addition formula, find the exact value of $\sin 75°$ .

Note: $75° = 45° + 30°$.

$\dfrac{\sqrt{6} - \sqrt{2}}{4}$

$\dfrac{\sqrt{6} + \sqrt{2}}{4}$

$\dfrac{\sqrt{3} + 1}{4}$

$\dfrac{\sqrt{2} + \sqrt{3}}{2}$

Find the exact value of $\cos 15°$ .

Note: $15° = 45° - 30°$.

$\dfrac{\sqrt{6} + \sqrt{2}}{4}$

$\dfrac{\sqrt{6} - \sqrt{2}}{4}$

$\dfrac{\sqrt{3} - 1}{4}$

$\dfrac{\sqrt{2} - \sqrt{6}}{4}$

Given $\sin A = \dfrac{3}{5}$ with angle $A$ in Quadrant I, find $\sin(2A)$ .

$\dfrac{9}{25}$

$\dfrac{6}{5}$

$\dfrac{24}{25}$

$\dfrac{3}{5}$

Which of the following is an equivalent form of $\cos(2A)$ written using only $\cos A$ ?

$2\cos^2 A - 1$

$1 - 2\cos^2 A$

$2\sin A \cos A$

$\cos^2 A + \sin^2 A$

Given $\sin A = \dfrac{3}{5}$ with angle $A$ in Quadrant I, find $\cos(2A)$ .

Enter your answer as a fraction (e.g., 7/25).

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HSF.TF.C.9 Tutor Intake -- Angle Addition and Double Angle Formulas

Concepts

Procedures