Trig Midterm

Front

What is the value of x if \(2x + 4 = 18\)?

Back

\(x = 7\)

Front

Define a co-terminal angle.

Back

Co-terminal angles are angles that share the same terminal side when drawn in standard position. They can be found by adding or subtracting multiples of \(360^\circ\) or \(2\pi\) radians.

Front

What is the formula for the sine of a sum of angles?

Back

\(\sin(a + b) = \sin a \cos b + \cos a \sin b\)

Front

What is the formula for the cosine of a difference of angles?

Back

\(\cos(a - b) = \cos a \cos b + \sin a \sin b\)

Front

How do you find the exact value of \(\sin(75^\circ)\)?

Back

Use the sum identity: \(\sin(75^\circ) = \sin(45^\circ + 30^\circ) = \sin 45^\circ \cos 30^\circ + \cos 45^\circ \sin 30^\circ = \frac{\sqrt{2}}{2} \cdot \frac{\sqrt{3}}{2} + \frac{\sqrt{2}}{2} \cdot \frac{1}{2} = \frac{\sqrt{6} + \sqrt{2}}{4}\)

Front

What is the amplitude of the function \(y = 3\sin x + 1\)?

Back

The amplitude is 3.

Front

What is the period of the function \(y = \sin(kx)\)?

Back

The period is \(\frac{2\pi}{k}\).

Front

What is the Pythagorean identity for sine and cosine?

Back

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

Front

How do you find the missing side of a right triangle using the Pythagorean theorem?

Back

If \(a\) and \(b\) are the legs and \(c\) is the hypotenuse, then \(c^2 = a^2 + b^2\).

Front

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

Back

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