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Trigonometric Values and Triangle Ratios
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Trigonometric Values and Triangle Ratios

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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?

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

What is the value of cos 60?

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

What is the value of cos 45?

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

What is the value of tan 30?

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

What is the value of tan 60?

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

What is the value of tan 45?

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

What is the value of csc 30?

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

What is the value of csc 60?

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

What is the value of csc 45?

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

What is the value of sec 30?

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

What is the value of sec 60?

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

What is the value of sec 45?

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

What is the value of cot 30?

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

What is the value of cot 60?

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

What is the value of cot 45?

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

What is the ratio of sides in a 30-60-90 triangle?

<p>1:2:√3</p> Signup and view all the answers

What is the ratio of sides in a 45-45-90 triangle?

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

What are the integral sides of the first common Pythagorean triple?

<p>3, 4, 5</p> Signup and view all the answers

What are the integral sides of the second common Pythagorean triple?

<p>5, 12, 13</p> Signup and view all the answers

What are the integral sides of the third common Pythagorean triple?

<p>8, 15, 17</p> Signup and view all the answers

What are the integral sides of the fourth common Pythagorean triple?

<p>7, 24, 25</p> Signup and view all the answers

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.

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