Sum and Difference Identities 2

Front

What is the formula for \( \sin(A - B) \)?

Back

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

Front

What is the formula for \( \cos(A - B) \)?

Back

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

Front

What is the formula for \( \tan(A - B) \)?

Back

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

Front

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

Back

\( \sin(90^\circ - A) = \cos A \) and \( \cos(90^\circ - A) = \sin A \)

Front

Expand \( \cos(A + B) \).

Back

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

Front

Expand \( \sin(A + B) \).

Back

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

Front

What is the value of \( \sin(180^\circ - A) \)?

Back

\( \sin(180^\circ - A) = \sin A \)

Front

What is the value of \( \cos(180^\circ - A) \)?

Back

\( \cos(180^\circ - A) = -\cos A \)

Front

What is the value of \( \tan(180^\circ - A) \)?

Back

\( \tan(180^\circ - A) = -\tan A \)

Front

If \( A = 30^\circ \) and \( B = 45^\circ \), what is \( \sin(A + B) \)?

Back

\( \sin(30^\circ + 45^\circ) = \sin(75^\circ) = \frac{\sqrt{6} + \sqrt{2}}{4} \)