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 $θ$ for each of the right triangles.

1.

$\tan θ =$

2.

$\tan θ =$

3.

$\tan θ =$

4.

$\tan θ =$

5.

In each graph, the angle of rotation is indicated by an arc and $θ$ . Describe the angles of rotation from $0$ to $2 π$ that make tangent $θ$ be positive and the angles of rotation that make tangent $θ$ be negative.

a.

Angles of rotation from $0$ to $2 π$ that make tangent $θ$ be positive:

b.

Angles of rotation from $0$ to $2 π$ that make tangent $θ$ be negative:

Set

6.

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$y = - 3 \sin (θ + \frac{π}{2})$
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$y = 3 \cos (θ + \frac{π}{2})$
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$y = \sin (2 (θ + \frac{π}{2})) - 2$
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$y = \sin (x + π)$

$y = - 3 \sin θ$
$y = - \sin θ$
$y = 2 \cos (θ + \frac{π}{2}) - 2$
$y = \cos (x + π) + 3$

7.

Select the equation(s) that have the same graph as $y = \cos θ$ .

A.

$y = \cos (- θ)$

B.

$y = \cos (θ - π)$

8.

Select the equation(s) that have the same graph as $y = - \sin θ$ .

A.

$y = \sin (θ + π)$

B.

$y = \sin (θ - π)$

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

9.

$f (t) = 150 \cos (\frac{π}{6} (t - 8)) + 80$

amplitude:

period:

horizontal shift:

vertical shift:

10.

$f (t) = 4.5 \sin (\frac{π}{4} t + \frac{3}{4}) + 8$

amplitude:

period:

horizontal shift:

vertical shift:

Go

For problems 11-14, multiply.

11.

$(7 - 6 i) (11 + 5 i)$

12.

$(10 + 3 i) (15 + i)$

13.

$(8 + 5 i) (8 - 5 i)$

14.

$(10 - i) (10 + i)$

15.

Find the quadratic equation with solutions $x = (8 + 5 i)$ and $x = (8 - 5 i)$ . Assume the coefficient of $x^{2}$ is 1.

16.

Find the quadratic equation with solutions $x = (10 + i)$ and $x = (10 - i)$ . Assume the coefficient of $x^{2}$ is 1.

17.

Find the quadratic equation with solutions $x = (6 + 3 i)$ and $x = (6 - 3 i)$ . Assume the coefficient of $x^{2}$ is 1.