Sum and Differences Review

Front

What is the cosine of an angle A if \( \cos A = \frac{3}{5} \) and \( 0 \degree \le A \le 90 \degree \)?

Back

\( \cos A = \frac{3}{5} \) means that in a right triangle, the adjacent side is 3 and the hypotenuse is 5.

Front

What is the sine of an angle B if \( \sin B = \frac{5}{13} \) and \( 90 \degree \le B \le 180 \degree \)?

Back

\( \sin B = \frac{5}{13} \) indicates that in a right triangle, the opposite side is 5 and the hypotenuse is 13.

Front

How do you find \( \cos(A+B) \) using the cosine addition formula?

Back

The formula is \( \cos(A+B) = \cos A \cos B - \sin A \sin B \).

Front

What is the value of \( \sin \frac{7\pi}{6} \)?

Back

\( \sin \frac{7\pi}{6} = -\frac{1}{2} \).

Front

How do you use sum or difference angle identities to find \( \cos 105^o \)?

Back

Use \( \cos(105^o) = \cos(60^o + 45^o) = \cos 60^o \cos 45^o - \sin 60^o \sin 45^o \).

Front

What is the solution to the equation \( \cos\left(\frac{\pi}{2}+x\right)-\sin\left(\frac{\pi}{2}+x\right)=0 \)?

Back

The solutions are \( x = \frac{3\pi}{4}, \frac{7\pi}{4} \).

Front

What is the sine addition formula?

Back

The sine addition formula is \( \sin(A+B) = \sin A \cos B + \cos A \sin B \).

Front

Evaluate \( \sin 150^o \).

Back

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

Front

What is the cosine of \( 90^o - A \)?

Back

\( \cos(90^o - A) = \sin A \).

Front

What is the sine of \( 90^o - B \)?

Back

\( \sin(90^o - B) = \cos B \).