Lesson 12
Tangent
- Let’s learn more about tangent.
Problem 1
Here is a graph of given by .
- Are and in the domain of ? Explain how you know.
- What are the -intercepts of the graph of ? Explain how you know.
Problem 2
The function is given by . Which of the statements are true? Select all that apply.
is a periodic function
The domain of is all real numbers.
The range of is all real numbers.
The period of is .
The period of is .
Problem 3
Here is the unit circle.
If where could angle be on the unit circle?
Problem 4
Here is a point on the unit circle.
- Explain why the line going through and has slope .
- What is the tangent of the angle represented by ? Explain how you know.
Problem 5
For which angles between 0 and is ? 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 is given by .
- Write an equation for the function whose graph is the graph of translated 3 units left and then reflected over the -axis.
- Write an equation for the function whose graph is the graph of reflected over the -axis and then translated 3 units to the left.
- Do and have the same graph? Explain your reasoning.