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Trigonometry, Unit Circle Pythagorean Identity - Cos/Sin to Identity (Radians, Typical Notation)

Level 1

This math topic encompasses problems on Trigonometry and the Unit Circle, specifically focusing on the Pythagorean Identity involving sine and cosine functions in radians. The questions task students with applying the identity to find relationships involving dimensions of triangles on the unit circle. Each problem presents a scenario requiring the use of the identity \( \sin^2(\theta) + \cos^2(\theta) = 1 \) to derive or verify expressions relating the sine and cosine values at specific angles, measured in radians. The skills practiced include understanding identities, manipulating algebraic expressions with trigonometric functions, and problem-solving using the unit circle.

Work on practice problems directly here, or download the printable pdf worksheet to practice offline.

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Trigonometry, Unit Circle Pythagorean Identity - Cos/Sin to Identity (Radians, Typical Notation) Worksheet

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Trigonometry, Unit Circle Pythagorean Identity - Cos/Sin to Identity ...
1
An svg image showing a math problem
What does Pythagoras tell us about the Y dimension of this triangle?
a A LaTex expression showing \sin{(Pi over 4 )} = square root of \cos to the power of 2 {(Pi over 4 ) + 1}
b A LaTex expression showing \sin{(Pi over 4 )} = square root of 1 - \cos to the power of 2 {(Pi over 4 )}
2
An svg image showing a math problem
What does Pythagoras tell us about the Y dimension of this triangle?
a A LaTex expression showing \sin to the power of 2 {(Pi over 3 )} = 1 - \cos to the power of 2 {(Pi over 3 )}
b A LaTex expression showing \sin to the power of 2 {(Pi over 3 )} = 1 + \cos to the power of 2 {(Pi over 3 )}
3
An svg image showing a math problem
What does Pythagoras tell us about the Y dimension of this triangle?
a A LaTex expression showing \sin to the power of 2 {(7Pi over 6 )} = 1 - \cos to the power of 2 {(7Pi over 6 )}
b A LaTex expression showing \sin to the power of 2 {(7Pi over 6 )} = 1 + \cos to the power of 2 {(7Pi over 6 )}
4
An svg image showing a math problem
What does Pythagoras tell us about the Y dimension of this triangle?
a A LaTex expression showing \sin{(7Pi over 4 )} = square root of \cos to the power of 2 {(7Pi over 4 ) + 1}
b A LaTex expression showing \sin{(7Pi over 4 )} = square root of 1 - \cos to the power of 2 {(7Pi over 4 )}
5
An svg image showing a math problem
What does Pythagoras tell us about the X dimension of this triangle?
a A LaTex expression showing \cos to the power of 2 {(11Pi over 6 )} = 1 + \sin to the power of 2 {(11Pi over 6 )}
b A LaTex expression showing \cos to the power of 2 {(11Pi over 6 )} = 1 - \sin to the power of 2 {(11Pi over 6 )}
6
An svg image showing a math problem
What does Pythagoras tell us about the X dimension of this triangle?
a A LaTex expression showing \cos{(2Pi over 3 )} = square root of \sin to the power of 2 {(2Pi over 3 ) + 1}
b A LaTex expression showing \cos{(2Pi over 3 )} = square root of 1 - \sin to the power of 2 {(2Pi over 3 )}
7
An svg image showing a math problem
What does Pythagoras tell us about the Y dimension of this triangle?
a A LaTex expression showing \sin{(Pi over 6 )} = square root of \cos to the power of 2 {(Pi over 6 ) + 1}
b A LaTex expression showing \sin{(Pi over 6 )} = square root of 1 - \cos to the power of 2 {(Pi over 6 )}
8
An svg image showing a math problem
What does Pythagoras tell us about the X dimension of this triangle?
a A LaTex expression showing \cos{(Pi over 4 )} = square root of 1 - \sin to the power of 2 {(Pi over 4 )}
b A LaTex expression showing \cos{(Pi over 4 )} = square root of \sin to the power of 2 {(Pi over 4 ) + 1}