chapter 7 review. solve for 0° ≤ θ ≤ 90° 1.) if tan θ = 2, find cot θ2.) if sin θ = ⅔,...

Chapter 7 Review

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Chapter 7 Review

Solve for 0° ≤ θ ≤ 90°

1.) If tan θ = 2, find cot θ 2.) if sin θ = ⅔, find cos θ

3.) If cos θ = ¼, find tan θ 4.) If tan θ = 3, find sec θ

5.) if sin θ = 7/10, find cot θ 6.) If tan θ = 7/2, find sin θ

Page 3: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Express each value as a function of an angle in Quadrant I

1.) sin 458° 2.) cos 892°

3.) tan (-876°) 4.) csc 495°

sin 82° -cos 8°

tan 24° csc 45°

Page 4: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Simplify1.) 2.)

3.) 4.)

Page 5: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Find a numerical value of one trig function.

1.) sin x = 3 cos x 2.) cos x = cot x

tan x = 3 csc x = 1

sin x = 1

Page 6: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Use the sum and difference identities to find the exact value of each function:1.) cos 75° 2.) cos 375° 3.) sin (-165°)

4.) sin (-105°) 5.) sin 95° cos 55° + cos 95° sin 55°

6.) tan (135° + 120°) 7.) tan 345°

Page 7: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

If α and β are the measures of two first quadrant angles, find the exact value of each function.

1.) if sin α = 12/13 and cos β = 3/5, find cos (α – β)

2.) if cos α = 12/13 and cos β = 12/37, find tan (α – β)

Page 8: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

If α and β are the measures of two first quadrant angles, find the exact value of each function.

3.) if cos α = 8/17 and tan β = 5/12, find cos (α + β)

4.) if csc α = 13/12 and sec β = 5/3, find sin (α – β)

Page 9: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

If sin A = 12/13, and A is in the first quadrant, find each value.

1.) cos 2A 2.) sin 2A

3.) tan 2A 4.) cos A/2

5.) sin A/2 6.) tan A/2

Page 10: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Use a half-angle identity to find the value of each

1.) 2.)

3.) 4.)

Page 11: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Solve for 0° ≤ x ≤ 180°

1.) 2.)

3.) 4.)

30°, 150° No solution, 270° is not in our domain

120° 60°

Page 12: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Solve for 0° ≤ x ≤ 180°

1.) 2.)

3.) 4.)

45°, 135° 0°

0°, 180° 0°, 90°, 180°

Page 13: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Solve for 0° ≤ x ≤ 180°

1.) 2.)

3.) 4.)

0° 30°, 150°

90° 0°, 135°, 180°

Page 14: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Solve for 0° ≤ x ≤ 180°

1.) 2.)

15°, 75° 0°, 30°, 150°, 180°

Page 15: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Write each equation in normal form. Then find the measure of the normal, p, and ϕ, the angle that the normal makes with the positive x-axis.

1.) 3x – 2y – 1 = 0 2.) 5x + y – 12 = 0

Page 16: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Write each equation in normal form. Then find the measure of the normal, p, and ϕ, the angle that the normal makes with the positive x-axis.

3.) y = x + 5 4.) y = x - 2

Page 17: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Write each equation in normal form. Then find the measure of the normal, p, and ϕ, the angle that the normal makes with the positive x-axis.

5.) x + y – 5 = 0 6.) 2x + y – 1 = 0

Page 18: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Write the standard form of the equation of the each line given “p”, and ϕ.

1.) p = 4, ϕ = 30° 2.) p = 2, ϕ = 45°

Page 19: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Write the standard form of the equation of the each line given “p”, and ϕ.

3.) p = 3, ϕ = 60° 4.) p = 12, ϕ = 120°

Page 20: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Write the standard form of the equation of the each line given “p”, and ϕ.

5.) p = 8, ϕ = 150° 2.) p = 15, ϕ = 225°

Page 21: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Find the distance between the point with the given coordinates and the line with the given equation.1.) (-1, 5), 3x – 4y – 1 = 02.) (2, 5), 5x – 12y + 1 = 0

3.) (1, -4), 12x + 5y – 3 = 0 4.) (-1,-3), 6x + 8y – 3 = 0

Page 22: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Find the distance between each equation.

1.) 2x – 3y + 4 = 0 2.) 4x – y + 1 = 0 y = ⅔x + 5 4x – y – 8 = 0

3.) x + 3y – 4 = 0 4.) 3x – 2y = 6 x + 3y + 20 = 0 3x – 2y + 30 = 0

(0, 4/3) (0, 1)

(0, 4/3) (0, -3)

Page 23: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Find an equation of the line that bisects the acute angle formed by the graphs of the equations x + 2y - 3 = 0 and x – y + 4 = 0

Page 24: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Find an equation of the line that bisects the acute angle formed by the graphs of the equations x + y – 5 = 0 and 2x – y + 7 = 0

Page 25: Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec

Find an equation of the line that bisects the acute angle formed by the graphs of the equations 2x + y – 3 = 0 and x – y + 5 = 0

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