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?

√3/2 Signup and view all the answers

What is the value of cos 60?

1/2 Signup and view all the answers

What is the value of cos 45?

√2/2 Signup and view all the answers

What is the value of tan 30?

√3/3 Signup and view all the answers

What is the value of tan 60?

√3 Signup and view all the answers

What is the value of tan 45?

1 Signup and view all the answers

What is the value of csc 30?

2 Signup and view all the answers

What is the value of csc 60?

2√3/3 Signup and view all the answers

What is the value of csc 45?

√2 Signup and view all the answers

What is the value of sec 30?

2√3/3 Signup and view all the answers

What is the value of sec 60?

2 Signup and view all the answers

What is the value of sec 45?

√2 Signup and view all the answers

What is the value of cot 30?

√3 Signup and view all the answers

What is the value of cot 60?

√3/3 Signup and view all the answers

What is the value of cot 45?

1 Signup and view all the answers

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

1:2:√3 Signup and view all the answers

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

1:1:√2 Signup and view all the answers

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

3, 4, 5 Signup and view all the answers

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

5, 12, 13 Signup and view all the answers

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

8, 15, 17 Signup and view all the answers

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

7, 24, 25 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.