Back to Exercise: Prove angle sum formulas

Exercises: Prove Angle Addition Formulas for Sine, Cosine, and Tangent

Show all steps for each problem. Express exact values as fractions or simplified radicals (do not give decimal approximations unless the problem asks for one).

Grade 9·23 problems·~35 min·Common Core Math - HS Functions·group·hsf-tf-c-9

Work through problems with immediate feedback

Warm-Up: Review What You Know

These problems review skills from earlier lessons.

What is the exact value of $\sin(30\degree)$ ?

$\frac{1}{2}$

$\frac{\sqrt{2}}{2}$

$\frac{\sqrt{3}}{2}$

$1$

What is the exact value of $\cos(45\degree)$ ?

$\frac{1}{2}$

$\frac{\sqrt{2}}{2}$

$\frac{\sqrt{3}}{2}$

$\frac{1}{\sqrt{3}}$

The Pythagorean identity says that for any angle $\theta$ :

$\sin(\theta) + \cos(\theta) = 1$

$\sin^2(\theta) + \cos^2(\theta) = 1$

$\sin^2(\theta) - \cos^2(\theta) = 1$

$\sin(\theta) \cdot \cos(\theta) = 1$

Fluency Practice

Which expression is equal to $\sin(A + B)$ ?

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

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

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

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

Which expression is equal to $\cos(A + B)$ ?

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

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

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

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

Use the addition formula to find the exact value of $\sin(75\degree)$ . Decompose $75\degree = 45\degree + 30\degree$ . Express your answer as a single simplified fraction with a radical numerator.

Find the exact value of $\cos(15\degree)$ . Use the decomposition $15\degree = 45\degree - 30\degree$ . Express your answer as a single simplified fraction with a radical numerator.

Which expression is equal to $\tan(A + B)$ ?

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

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

$\frac{\tan(A) + \tan(B)}{1 + \tan(A)\tan(B)}$

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

You're viewing 2 of 6 sections.

Create a free account to continue the full exercise set and save your progress.

Create free account

0 of 8 answered

Answer all problems to submit.