Lesson 12
Tangent
- Let’s learn more about tangent.
Problem 1
Here is a graph of f given by f(\theta) = \tan(\theta).
- Are \frac{\pi}{2} and \frac{3\pi}{2} in the domain of f? Explain how you know.
- What are the \theta-intercepts of the graph of f? Explain how you know.
Problem 2
The function f is given by f(\theta) = \tan(\theta). Which of the statements are true? Select all that apply.
f is a periodic function
The domain of f is all real numbers.
The range of f is all real numbers.
The period of f is 2\pi.
The period of f is \pi.
Problem 3
Here is the unit circle.
If \tan(a) > 1 where could angle a be on the unit circle?
Problem 4
Here is a point on the unit circle.
- Explain why the line going through (0,0) and P has slope \frac{1}{2}.
- What is the tangent of the angle represented by P? Explain how you know.
Problem 5
For which angles \theta between 0 and 2\pi is \cos(\theta) < 0? Explain how you know.
Problem 6
It is 3:00 a.m.
- What angle will the hour hand rotate through in the next hour? Explain how you know.
- What angle will the hour hand rotate through in the next 12 hours? Explain how you know.
- What angle will the hour hand rotate through in the next 24 hours? Explain how you know.
Problem 7
The function f is given by f(x) = x^2.
- Write an equation for the function g whose graph is the graph of f translated 3 units left and then reflected over the y-axis.
- Write an equation for the function h whose graph is the graph of f reflected over the y-axis and then translated 3 units to the left.
- Do g and h have the same graph? Explain your reasoning.