Lesson 3 Getting on the Right Wavelength Practice Understanding

Ready

Use what you know about the definition of tangent in a right triangle to find the value of tangent for each of the right triangles.

1.

a circle is graphed on a coordinate plane. A ray is drawn from the center to the point (4,3) creating a right angle on the x axis and an undetermined angle in the center. (4, 3)

2.

a circle is graphed on a coordinate plane. A ray is drawn from the center to the point (-16,63) creating a right angle on the x axis and an undetermined angle in the center. (-16, 63)AF

3.

a circle is graphed on a coordinate plane. A ray is drawn from the center to the point (-7,-7) creating a right angle on the x axis and an undetermined angle in the center. FA(-7,-7)

4.

a circle is graphed on a coordinate plane. A ray is drawn from the center to the point (2 time the square root of 3, - 2) creating a right angle on the x axis and an undetermined angle in the center. AF

5.

In each graph, the angle of rotation is indicated by an arc and . Describe the angles of rotation from to that make tangent be positive and the angles of rotation that make tangent be negative.

a.

Angles of rotation from to that make tangent be positive:

b.

Angles of rotation from to that make tangent be negative:

Set

6.

Match each trigonometric representation with an equivalent representation. Then, check your answers with a graphing calculator.

(The scale on the vertical axis is . The scale on the horizontal axis is .)

  1. ___

  2. ___

  3. ___

    a wide sine function is graphed on a coordinate plane with a point at (0,2) x–3π / 2–3π / 2–3π / 2–π–π–π–π / 2–π / 2–π / 2π / 2π / 2π / 2πππ3π / 23π / 23π / 2y222444000
  4. ___

    a cosine function is graphed on a coordinate plane with a point at (0,-2) x–2π–2π–2π–3π / 2–3π / 2–3π / 2–π–π–π–π / 2–π / 2–π / 2π / 2π / 2π / 2πππ3π / 23π / 23π / 2y–4–4–4–2–2–2222000
  5. ___

  6. ___

  1. a sine function is graphed on a coordinate plane with a point at (0,-3) x–2π–2π–2π–3π / 2–3π / 2–3π / 2–π–π–π–π / 2–π / 2–π / 2π / 2π / 2π / 2πππ3π / 23π / 23π / 2y–4–4–4–2–2–2222444000
  2. a cosine function is graphed on a coordinate plane with a point at (0,-2) and a small amplitude x–2π–2π–2π–3π / 2–3π / 2–3π / 2–π–π–π–π / 2–π / 2–π / 2π / 2π / 2π / 2πππ3π / 23π / 23π / 2y–4–4–4–2–2–2222444000

7.

Select the equation(s) that have the same graph as .

A.

B.

8.

Select the equation(s) that have the same graph as .

A.

B.

For each function, identify the amplitude, period, horizontal shift, and vertical shift.

9.

amplitude:

period:

horizontal shift:

vertical shift:

10.

amplitude:

period:

horizontal shift:

vertical shift:

Go

For problems 11-14, multiply.

11.

12.

13.

14.

15.

Find the quadratic equation with solutions and . Assume the coefficient of is 1.

16.

Find the quadratic equation with solutions and . Assume the coefficient of is 1.

17.

Find the quadratic equation with solutions and . Assume the coefficient of is 1.