Questions and Answers
What is the value of sin 30?
1/2
What is the value of sin 60?
√3/2
What is the value of sin 45?
√2/2
What is the value of cos 30?
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What is the value of cos 60?
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What is the value of cos 45?
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What is the value of tan 30?
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What is the value of tan 60?
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What is the value of tan 45?
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What is the value of csc 30?
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What is the value of csc 60?
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What is the value of csc 45?
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What is the value of sec 30?
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What is the value of sec 60?
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What is the value of sec 45?
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What is the value of cot 30?
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What is the value of cot 60?
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What is the value of cot 45?
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What is the ratio of sides in a 30-60-90 triangle?
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What is the ratio of sides in a 45-45-90 triangle?
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What are the integral sides of the first common Pythagorean triple?
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What are the integral sides of the second common Pythagorean triple?
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What are the integral sides of the third common Pythagorean triple?
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What are the integral sides of the fourth common Pythagorean triple?
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Study Notes
Trigonometric Values for Special Angles
- sin 30° = 1/2
- sin 60° = √3/2
- sin 45° = √2/2
- cos 30° = √3/2
- cos 60° = 1/2
- cos 45° = √2/2
- tan 30° = √3/3
- tan 60° = √3
- tan 45° = 1
Cosecant, Secant, and Cotangent Values
- csc 30° = 2 (inverse of sin 30°)
- csc 60° = 2√3/3 (inverse of sin 60°)
- csc 45° = √2 (inverse of sin 45°)
- sec 30° = 2√3/3 (inverse of cos 30°)
- sec 60° = 2 (inverse of cos 60°)
- sec 45° = √2 (inverse of cos 45°)
- cot 30° = √3 (inverse of tan 30°)
- cot 60° = √3/3 (inverse of tan 60°)
- cot 45° = 1 (inverse of tan 45°)
30-60-90 Triangle Ratio
- Ratios of sides in a 30-60-90 triangle are in the proportion 1:2:√3.
45-45-90 Triangle Ratio
- Ratios of sides in a 45-45-90 triangle are in the proportion 1:1:√2.
Integral Lengths of Pythagorean Triples
- First Triple: 3, 4, 5
- Second Triple: 5, 12, 13
- Third Triple: 8, 15, 17
- Fourth Triple: 7, 24, 25
Key Concepts
- Special angles in trigonometry have fixed sine, cosine, and tangent values.
- Cosecant, secant, and cotangent functions are used for their respective angles.
- Understanding Pythagorean triples is essential for solving problems involving right triangles with integral side lengths.
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Description
This quiz covers essential trigonometric values for special angles, including sine, cosine, tangent, and their inverses. Additionally, you'll learn about the side ratios of the 30-60-90 and 45-45-90 triangles, along with integral lengths of Pythagorean triples. Test your knowledge on these foundational concepts in trigonometry.
