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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) (D) Signup and view all the answers

What is the reciprocal identity for secant?

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

What is the co-function identity for sine?

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

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

Cosecant (D) Signup and view all the answers

What are the trigonometric identities based on?

All six trigonometric functions (B) Signup and view all the answers

Which of the following is NOT a trigonometric function?

Quotient (D) Signup and view all the answers

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

Right triangles (D) Signup and view all the answers

What do the trigonometric identities involve?

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

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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).