Algebra 2 | Unit 6 | Lesson 9: Introduction to Trigonometric Functions | Practice Problems

Which statement is not true for the function \(f\) given by \(f(\theta) = \sin(\theta)\), for values of \(\theta\) between 0 and \(2\pi\)?

• The outputs of the function range from -1 to 1.

• \(\sin{\theta} = 1\) only when \(\theta = \frac{\pi}{2}\)

• \(\sin{\theta} = 0\) only when \(\theta = 0\)

• \(\sin{\theta} > 0\) for \(0 < \theta < \pi\)

Angle \(\theta\), measured in radians, satisfies \(\cos(\theta) = 0\). What could the value of \(\theta\) be? Select all that apply.

• 0

• \(\frac{\pi}{4}\)

• \(\frac{\pi}{2}\)

• \(\pi\)

• \(\frac{3\pi}{2}\)

Here are the graphs of two functions. Which is the graph of \(y = \cos(\theta)\)? Explain how you know.

Here are the graphs of two functions. Which is the graph of \(y = \sin(\theta)\)? Explain how you know.

Which statements are true for both functions \(y = \cos(\theta)\) and \(y = \sin(\theta)\)? Select all that apply.

• The function has a value of about 0.71 when \(\theta = \frac{\pi}{4}\).

• The maximum value is 1.

• The function is periodic.

• The period of the function is \(2\pi\).

• The maximum value occurs at \(\theta = 0\).

Here is a graph of a function \(f\). The function \(f\) is either defined by \(f(\theta) = \cos^2(\theta) + \sin^2(\theta)\) or \(f(\theta) = \cos^2(\theta) - \sin^2(\theta)\). Which definition is correct? Explain how you know.

The minute hand on a clock is 1.5 feet long. The end of the minute hand is 6 feet above the ground at one time each hour. How many feet above the ground could the center of the clock be? Select all that apply.

• 4.5

• 5

• 6

• 7

• 7.5

Here is a graph of the water level height, \(h\), in feet, relative to a fixed mark, measured at a beach over several days \(d\). Explain why the water level is a function of time.

Here is a graph of the water level height, \(h\), in feet, relative to a fixed mark, measured at a beach over several days \(d\). Describe how the water level varies each day.

Here is a graph of the water level height, \(h\), in feet, relative to a fixed mark, measured at a beach over several days \(d\). What does it mean in this context for the water level to be a periodic function of time?