Questions and Answers
What is sin(0°)?
0
What is cos(0°)?
1
What is tan(0°)?
0
What is sin(30°)?
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What is cos(30°)?
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What is tan(30°)?
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What is sin(45°)?
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What is cos(45°)?
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What is tan(45°)?
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What is sin(60°)?
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What is cos(60°)?
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What is tan(60°)?
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What is sin(90°)?
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What is cos(90°)?
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What is tan(90°)?
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What is sin(180°)?
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What is cos(180°)?
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What is tan(180°)?
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What is sin(270°)?
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What is cos(270°)?
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What is tan(270°)?
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What is sin(360°)?
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What is cos(360°)?
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What is tan(360°)?
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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?
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What is cos θ?
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What is tan θ?
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What is csc θ?
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What is sec θ?
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What is cot θ?
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What is θ?
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What is standard position?
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What are reference angles?
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What are coterminal angles?
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Which quadrants have positive cosine?
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Which quadrants have negative cosine?
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Which quadrants have positive sine?
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Which quadrants have negative sine?
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How to convert to radians?
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How to convert to degrees?
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What is 0 divided by any number?
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What is any number divided by zero?
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What is any number divided by one?
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What is 0° in radians?
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What is 30° in radians?
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What is 45° in radians?
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What is 60° in radians?
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What is 90° in radians?
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What is 120° in radians?
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What is 135° in radians?
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What is 150° in radians?
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What is 180° in radians?
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What is 210° in radians?
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What is 225° in radians?
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What is 240° in radians?
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What is 270° in radians?
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What is 300° in radians?
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What is 315° in radians?
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What is 330° in radians?
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What is 360° in radians?
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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.
