Trig Sum and Difference Identities

Front

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

Back

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

Tags

CCSS.HSF.TF.C.9

Front

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

Back

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

Tags

CCSS.HSF.TF.C.9

Front

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

Back

\( \tan(\alpha + \beta) = \frac{\tan\alpha + \tan\beta}{1 - \tan\alpha \tan\beta} \)

Tags

CCSS.HSF.TF.C.9

Front

What is the sine of \( 150^{\circ} \)?

Back

\( \sin(150^{\circ}) = \frac{1}{2} \)

Tags

CCSS.HSF.TF.A.2

Front

What is the cosine of \( 120^{\circ} \)?

Back

\( \cos(120^{\circ}) = -\frac{1}{2} \)

Tags

CCSS.HSF.TF.A.2

Front

What is the relationship between sine and cosine for complementary angles?

Back

\( \sin(\theta) = \cos(90^{\circ} - \theta) \)

Tags

CCSS.HSG.SRT.C.7

Front

What is the value of \( \sin(37^{\circ}) \cos(113^{\circ}) + \cos(37^{\circ}) \sin(113^{\circ}) \)?

Back

\( \sin(150^{\circ}) = \frac{1}{2} \)

Tags

CCSS.HSF.TF.C.9

Front

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

Back

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

Tags

CCSS.HSF.TF.C.9

Front

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

Back

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

Tags

CCSS.HSF.TF.C.9

Front

What is the value of \( \tan(45^{\circ}) \)?

Back

\( \tan(45^{\circ}) = 1 \)

Tags

CCSS.HSF.TF.A.2