Sum and Difference Formulas

Front

What is the formula for \( \cos(\alpha - \beta) \)?

Back

\( \cos(\alpha - \beta) = \cos\alpha \cos\beta + \sin\alpha \sin\beta \)

Front

Expand \( \sin(33^{\circ} + 42^{\circ}) \).

Back

\( \sin(33^{\circ}) \cos(42^{\circ}) + \cos(33^{\circ}) \sin(42^{\circ}) \)

Front

What is the Pythagorean identity for sine and cosine?

Back

\( \cos^2 x + \sin^2 x = 1 \)

Front

Given \( \tan \alpha = \frac{3}{4} \) and \( \tan \beta = -\frac{1}{2} \), how do you find \( \tan(\alpha - \beta) \)?

Back

Use the formula: \( \tan(\alpha - \beta) = \frac{\tan \alpha - \tan \beta}{1 + \tan \alpha \tan \beta} \)

Front

What is the value of \( \tan(105^{\circ}) \)?

Back

\( \tan(105^{\circ}) = -2 - \sqrt{3} \)

Front

What is the formula for \( \sin(\alpha + \beta) \)?

Back

\( \sin(\alpha + \beta) = \sin \alpha \cos \beta + \cos \alpha \sin \beta \)

Front

What is the formula for \( \cos(\alpha + \beta) \)?

Back

\( \cos(\alpha + \beta) = \cos \alpha \cos \beta - \sin \alpha \sin \beta \)

Front

What is the relationship between tangent and sine/cosine?

Back

\( \tan x = \frac{\sin x}{\cos x} \)

Front

What is the double angle formula for sine?

Back

\( \sin(2x) = 2 \sin x \cos x \)

Front

What is the double angle formula for cosine?

Back

\( \cos(2x) = \cos^2 x - \sin^2 x \)