Trigonometric Identities - Concept

Concept Concept (1)

Identities are equations true for any value of the variable. Since a right triangle drawn in the unit circle has a hypotenuse of length 1, we define the trigonometric identies x=cos(theta) and y=sin(theta). In the same triangle, tan(theta)=x/y, so substituting we get tan(theta)=sin(theta)/cos(theta), the tangent identity. Another key trigonometric identity sin2(theta) + cos2(theta)=1 comes from using the unit circle and the Pythagorean Theorem.

Sample Sample Problems (3)

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Trigonometric Identities - Problem 1
Problem 1
How to use the Pythagorean identity to find cosine and tangent when sine is known.
Trigonometric Identities - Problem 2
Problem 2
How to use the unit circle to show that cosine is an even function, and sine and tangent are odd functions.
Trigonometric Identities - Problem 3
Problem 3
How to use the unit circle to show that sine and cosine have period 2*pi, and tangent has period pi.