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Trigonometric Functions and Identities Quiz

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Trigonometric Functions and Identities Quiz

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Questions and Answers

What is the Pythagorean identity for sine and cosine?

$cos^2(x) = 1 - sin^2(x)$

$sin^2(x) - cos^2(x) = 1$

$sin^2(x) + cos^2(x) = 1$ (correct)

$sin^2(x) = 1 - cos^2(x)$

What is the double angle identity for sine?

$sin(2x) = cos^2(x) - sin^2(x)$

$sin(2x) = 2sin(x)cos(x)$ (correct)

$sin(2x) = sin^2(x) - cos^2(x)$

$sin(2x) = 2cos(x)sin(x)$

What is the half angle identity for cosine?

$cos^2(x/2) = (1 + sin(x))/2$

$cos^2(x/2) = (1 + cos(x))/2$ (correct)

$cos^2(x/2) = (1 - cos(x))/2$

$cos^2(x/2) = (1 - sin(x))/2$

What is the trigonometric identity for tangent in terms of sine and cosine?

tan(x) = sin(x) / cos(x) Signup and view all the answers

What is the reciprocal identity for secant?

sec(x) = 1 / cos(x) Signup and view all the answers

What is the co-function identity for sine?

sin(x) = cos(90 - x) Signup and view all the answers

Which of the following is NOT one of the primary trigonometric functions?

Cosecant Signup and view all the answers

What are the trigonometric identities based on?

All six trigonometric functions Signup and view all the answers

Which of the following is NOT a trigonometric function?

Quotient Signup and view all the answers

For which type of triangles do the trigonometric identities hold true?

Right triangles Signup and view all the answers

What do the trigonometric identities involve?

Both the side lengths and the angles of a triangle Signup and view all the answers

Study Notes

Trigonometric Identities

The Pythagorean identity for sine and cosine is sin²(x) + cos²(x) = 1.
The double angle identity for sine is sin(2x) = 2sin(x)cos(x).
The half angle identity for cosine is cos(x/2) = ±√((1 + cos(x))/2).

Trigonometric Functions

The trigonometric identity for tangent in terms of sine and cosine is tan(x) = sin(x)/cos(x).
The reciprocal identity for secant is sec(x) = 1/cos(x).

Co-Function Identity

The co-function identity for sine is sin(π/2 - x) = cos(x).

Primary Trigonometric Functions

The primary trigonometric functions are sine, cosine, tangent, cotangent, secant, and cosecant.
The primary trigonometric functions do not include versine.

Bases of Trigonometric Identities

Trigonometric identities are based on the ratios of sides in right-angled triangles.

Types of Triangles

Trigonometric identities hold true for right-angled triangles.

Trigonometric Identities Involvement

Trigonometric identities involve the relationships between the angles and side lengths of right-angled triangles.

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Description

Test your knowledge of trigonometric functions and identities with this comprehensive quiz. From reciprocal and Pythagorean identities to sum and difference of angles and product-sum identities, this quiz covers a wide range of topics in trigonometry. Challenge yourself and see how well you understand these fundamental concepts.