Miller - Review 3.1 - 3.3 Trig Intro

Front

What is the period of a sine or cosine function?

Back

The period of a sine or cosine function is the distance along the x-axis over which the function completes one full cycle. For the standard functions, the period is given by the formula \( P = \frac{2\pi}{|b|} \), where \( b \) is the coefficient of \( x \) in the function \( f(x) = a \sin(bx + c) + d \) or \( f(x) = a \cos(bx + c) + d \).

Front

Find the period of the function \( f(x) = 3 \sin(2x) \).

Back

The period is \( P = \frac{2\pi}{|2|} = \pi \).

Front

What is \( \cos(0) \)?

Back

\( \cos(0) = 1 \).

Front

What is the value of \( \cos(\frac{3\pi}{4}) \)?

Back

\( \cos(\frac{3\pi}{4}) = -\frac{\sqrt{2}}{2} \).

Front

Define the unit circle.

Back

The unit circle is a circle with a radius of 1 centered at the origin of the coordinate plane. It is used to define trigonometric functions for all angles.

Front

What is the value of \( \sin(90^{\circ}) \)?

Back

\( \sin(90^{\circ}) = 1 \).

Front

What is the relationship between sine and cosine?

Back

The sine and cosine functions are related by the identity \( \sin^2(\theta) + \cos^2(\theta) = 1 \).

Front

Find \( \cos(\theta) \) if the point on the unit circle is (\( \frac{3}{5}, \frac{4}{5} \)).

Back

\( \cos(\theta) = \frac{3}{5} \).

Front

What is the value of \( \sin(30^{\circ}) \)?

Back

\( \sin(30^{\circ}) = \frac{1}{2} \).

Front

What is the period of the function \( f(x) = 2 \cos(3x) \)?

Back

The period is \( P = \frac{2\pi}{|3|} = \frac{2\pi}{3} \).