Advanced Algebra/Trig Final Exam Study Guide
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Questions and Answers

What is sin(0°)?

0

What is cos(0°)?

1

What is tan(0°)?

0

What is sin(30°)?

<p>1/2</p> Signup and view all the answers

What is cos(30°)?

<p>√3/2</p> Signup and view all the answers

What is tan(30°)?

<p>√3/3</p> Signup and view all the answers

What is sin(45°)?

<p>√2/2</p> Signup and view all the answers

What is cos(45°)?

<p>√2/2</p> Signup and view all the answers

What is tan(45°)?

<p>1</p> Signup and view all the answers

What is sin(60°)?

<p>√3/2</p> Signup and view all the answers

What is cos(60°)?

<p>1/2</p> Signup and view all the answers

What is tan(60°)?

<p>√3</p> Signup and view all the answers

What is sin(90°)?

<p>1</p> Signup and view all the answers

What is cos(90°)?

<p>0</p> Signup and view all the answers

What is tan(90°)?

<p>undefined</p> Signup and view all the answers

What is sin(180°)?

<p>0</p> Signup and view all the answers

What is cos(180°)?

<p>-1</p> Signup and view all the answers

What is tan(180°)?

<p>0</p> Signup and view all the answers

What is sin(270°)?

<p>-1</p> Signup and view all the answers

What is cos(270°)?

<p>0</p> Signup and view all the answers

What is tan(270°)?

<p>undefined</p> Signup and view all the answers

What is sin(360°)?

<p>0</p> Signup and view all the answers

What is cos(360°)?

<p>1</p> Signup and view all the answers

What is tan(360°)?

<p>0</p> Signup and view all the answers

What is the Law of Sines?

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What is the Law of Cosines?

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What is the area of an oblique triangle?

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What does 0 solutions mean?

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What does 1 solution mean?

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What does 2 solutions mean?

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What is sin θ?

<p>y coordinate of angle θ on the unit circle</p> Signup and view all the answers

What is cos θ?

<p>x coordinate of angle θ on the unit circle</p> Signup and view all the answers

What is tan θ?

<p>sin θ / cos θ</p> Signup and view all the answers

What is csc θ?

<p>reciprocal of sine</p> Signup and view all the answers

What is sec θ?

<p>reciprocal of cosine</p> Signup and view all the answers

What is cot θ?

<p>reciprocal of tangent</p> Signup and view all the answers

What is θ?

<p>the angle in question</p> Signup and view all the answers

What is standard position?

<p>angle begins on the positive x axis at 0</p> Signup and view all the answers

What are reference angles?

<p>always a positive number</p> Signup and view all the answers

What are coterminal angles?

<p>add 2π or 360° and subtract 2π or 360°</p> Signup and view all the answers

Which quadrants have positive cosine?

<ul> <li>Q1, Q4</li> </ul> Signup and view all the answers

Which quadrants have negative cosine?

<ul> <li>Q2, Q3</li> </ul> Signup and view all the answers

Which quadrants have positive sine?

<ul> <li>Q1, Q2</li> </ul> Signup and view all the answers

Which quadrants have negative sine?

<ul> <li>Q3, Q4</li> </ul> Signup and view all the answers

How to convert to radians?

<p>multiply by π/180</p> Signup and view all the answers

How to convert to degrees?

<p>multiply by 180/π</p> Signup and view all the answers

What is 0 divided by any number?

<p>0</p> Signup and view all the answers

What is any number divided by zero?

<p>undefined</p> Signup and view all the answers

What is any number divided by one?

<p>itself</p> Signup and view all the answers

What is 0° in radians?

<p>0</p> Signup and view all the answers

What is 30° in radians?

<p>π/6</p> Signup and view all the answers

What is 45° in radians?

<p>π/4</p> Signup and view all the answers

What is 60° in radians?

<p>π/3</p> Signup and view all the answers

What is 90° in radians?

<p>π/2</p> Signup and view all the answers

What is 120° in radians?

<p>2π/3</p> Signup and view all the answers

What is 135° in radians?

<p>3π/4</p> Signup and view all the answers

What is 150° in radians?

<p>5π/6</p> Signup and view all the answers

What is 180° in radians?

<p>π</p> Signup and view all the answers

What is 210° in radians?

<p>7π/6</p> Signup and view all the answers

What is 225° in radians?

<p>5π/4</p> Signup and view all the answers

What is 240° in radians?

<p>4π/3</p> Signup and view all the answers

What is 270° in radians?

<p>3π/2</p> Signup and view all the answers

What is 300° in radians?

<p>5π/3</p> Signup and view all the answers

What is 315° in radians?

<p>7π/4</p> Signup and view all the answers

What is 330° in radians?

<p>11π/6</p> Signup and view all the answers

What is 360° in radians?

<p>2π</p> Signup and view all the answers

Study Notes

Trigonometric Values for Key Angles

  • sin(0°) = 0
  • cos(0°) = 1
  • tan(0°) = 0
  • sin(30°) = 1/2
  • cos(30°) = √3/2
  • tan(30°) = √3/3
  • sin(45°) = √2/2
  • cos(45°) = √2/2
  • tan(45°) = 1
  • sin(60°) = √3/2
  • cos(60°) = 1/2
  • tan(60°) = √3
  • sin(90°) = 1
  • cos(90°) = 0
  • tan(90°) = undefined
  • sin(180°) = 0
  • cos(180°) = -1
  • tan(180°) = 0
  • sin(270°) = -1
  • cos(270°) = 0
  • tan(270°) = undefined
  • sin(360°) = 0
  • cos(360°) = 1
  • tan(360°) = 0

Special Angles in Radians

  • 0° = 0
  • 30° = π/6
  • 45° = π/4
  • 60° = π/3
  • 90° = π/2
  • 120° = 2π/3
  • 135° = 3π/4
  • 150° = 5π/6
  • 180° = π
  • 210° = 7π/6
  • 225° = 5π/4
  • 240° = 4π/3
  • 270° = 3π/2
  • 300° = 5π/3
  • 315° = 7π/4
  • 330° = 11π/6
  • 360° = 2π

Trigonometric Function Definitions

  • sin(θ) = y-coordinate of angle θ on the unit circle
  • cos(θ) = x-coordinate of angle θ on the unit circle
  • tan(θ) = sin(θ) / cos(θ)
  • csc(θ) = 1/sin(θ) (reciprocal of sine)
  • sec(θ) = 1/cos(θ) (reciprocal of cosine)
  • cot(θ) = 1/tan(θ) (reciprocal of tangent)

Angle Properties

  • θ represents the angle in question
  • Standard position refers to an angle starting on the positive x-axis at 0°
  • Reference angles are positive and are the smallest angle made with the x-axis
  • Coterminal angles are found by adding or subtracting 2π or 360°

Quadrants and Sign of Functions

  • Cosine is positive in Quadrants I and IV; negative in II and III
  • Sine is positive in Quadrants I and II; negative in III and IV

Conversion Formulas

  • Convert degrees to radians: multiply by π/180
  • Convert radians to degrees: multiply by 180/π

Division Notations

  • Zero divided by any number = 0
  • Any number divided by zero = undefined
  • Any number divided by one = itself

Solutions of Triangles

  • Categories based on solutions:
    • 0 solutions: conditions prevent triangle formation
    • 1 solution: unique triangle can be formed
    • 2 solutions: two possible triangles can exist based on the given criteria

Area of Oblique Triangle

  • Area calculations may involve specific formulas, typically including side lengths and angles.

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Description

Prepare for your Advanced Algebra and Trigonometry final exam with this comprehensive study guide. This set includes essential formulas and values for various trigonometric functions, helping you solidify your understanding and excel in your exam.

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