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Trigonometry, Unit Circle Pythagorean Identity - Dimension to Cos/Sin Value Identity, Degrees

Level 1

This math topic focuses on the application of trigonometric Pythagorean identities within the context of the unit circle. Specifically, it helps learners understand how to relate the X and Y dimensions (cosine and sine values) of a triangle to degrees using Pythagorean identities. The problems involve finding expressions for cosine and sine values based on given angles, leveraging the Pythagorean theorem's relationship between different sides of a right triangle within the unit circle. This is a foundational component of trigonometry and unit circle theory, tailored for practice at an introductory level.

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

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Trigonometry, Unit Circle Pythagorean Identity - Dimension to Cos/Sin Value Identity, Degrees Worksheet

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Trigonometry, Unit Circle Pythagorean Identity - Dimension to Cos/Sin...
1
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{(225 to the power of circle )} = square root of 1 - (-\frac{\sqrt{2}{2}) to the power of 2 }
b A LaTex expression showing \cos{(225 to the power of circle )} = square root of (-\frac{\sqrt{2}{2}) to the power of 2 + 1}
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 {(240 to the power of circle )} = 1 + (-1 over 2 ) to the power of 2
b A LaTex expression showing \sin to the power of 2 {(240 to the power of circle )} = 1 - (-1 over 2 ) to the power of 2
3
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{(120 to the power of circle )} = square root of 1 - (\frac{\sqrt{3}{2}) to the power of 2 }
b A LaTex expression showing \cos{(120 to the power of circle )} = square root of (\frac{\sqrt{3}{2}) to the power of 2 + 1}
4
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{(60 to the power of circle )} = square root of (\frac{\sqrt{3}{2}) to the power of 2 + 1}
b A LaTex expression showing \cos{(60 to the power of circle )} = square root of 1 - (\frac{\sqrt{3}{2}) to the power of 2 }
5
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 {(135 to the power of circle )} = 1 - (-\frac{square root of 2}{2}) to the power of 2
b A LaTex expression showing \sin to the power of 2 {(135 to the power of circle )} = 1 + (-\frac{square root of 2}{2}) to the power of 2
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 to the power of 2 {(225 to the power of circle )} = 1 - (-\frac{square root of 2}{2}) to the power of 2
b A LaTex expression showing \cos to the power of 2 {(225 to the power of circle )} = 1 + (-\frac{square root of 2}{2}) to the power of 2
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 to the power of 2 {(60 to the power of circle )} = 1 - (1 over 2 ) to the power of 2
b A LaTex expression showing \sin to the power of 2 {(60 to the power of circle )} = 1 + (1 over 2 ) to the power of 2
8
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 {(210 to the power of circle )} = 1 + (-\frac{square root of 3}{2}) to the power of 2
b A LaTex expression showing \sin to the power of 2 {(210 to the power of circle )} = 1 - (-\frac{square root of 3}{2}) to the power of 2