Lesson 4 Off on a Tangent Develop Understanding

Ready

The equation of a parent function is given. Write a new equation with the given transformations. Then sketch the new function on the same graph as the parent function. (If the function has asymptotes, sketch them in.)

1.

  • vertical shift: up

  • horizontal shift: left

  • vertical stretch or shrink:

Equation:

Graph:

graph of y=x^2 x–4–4–4–2–2–2222444y555101010151515000

2.

  • vertical shift: up

  • horizontal shift: right

  • vertical stretch or shrink:

a.

Equation:

b.

graph of y=1/x x–4–4–4–2–2–2222444y–5–5–5555000

3.

  • vertical shift: none

  • horizontal shift: left

  • vertical stretch or shrink:

a.

Equation:

b.

graph of y=radical x x–8–8–8–6–6–6–4–4–4–2–2–2222444666888y–5–5–5555000

4.

  • vertical shift:

  • horizontal shift: left

  • vertical stretch or shrink (amplitude):

a.

Equation:

b.

graph of y=sin x xπππy–2–2–2222444000

Set

5.

Triangle is a right triangle. .

Use the information in the figure to label the length of the sides and measure of the angles.

Isosceles right Triangle ABC ABC

6.

Triangle is an equilateral triangle. and is an altitude.

Use the information in the figure to label the length of the sides, the length of , and the exact length of .

Label the measure of angles and .

Triangle RST with altitude SA SRAT

7.

Use what you know about the unit circle and the information from the figures in to fill in the table.

function

8.

Label all of the points and angles of rotation in the unit circle.

a blank unit circle

9.

Fill in the chart for .

10.

Explain how the answers in problem 9 support the statement that is classified as an odd function.

Go

Answer the questions. Be sure you can justify your thinking.

11.

Given triangle with angle being a right angle, what is ?

12.

Identify the quadrants in which is positive.

13.

Identify the quadrants in which is negative.

14.

Identify the quadrants in which is positive.

15.

Explain why it is impossible for .

16.

Name the angles of rotation (in radians) for when .

17.

For which trigonometric function does a positive rotation and a negative rotation always give the same value?

18.

Explain why in the unit circle, .

19.

Explain why .