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

Level 1

This math topic covers Trigonometry, focusing on the Unit Circle and Pythagorean identities, transforming dimensions to cosine or sine values, and utilizing radians. It specifically guides learners on how to use Pythagoras' theorem to determine the x and y dimensions (or measurements) of triangles within the unit circle. The worksheet presents various problem scenarios using radians and asks for applications of the sine and cosine identities derived from the Pythagorean theorem. Each question provides multiple-choice answers involving algebraic expressions of trigonometric calculations.

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, Radians 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{(Pi over 3 )} = square root of 1 - (\frac{\sqrt{3}{2}) to the power of 2 }
b A LaTex expression showing \cos{(Pi over 3 )} = square root of (\frac{\sqrt{3}{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 {(4Pi over 3 )} = 1 - (-1 over 2 ) to the power of 2
b A LaTex expression showing \sin to the power of 2 {(4Pi over 3 )} = 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 to the power of 2 {(3Pi over 4 )} = 1 - (\frac{square root of 2}{2}) to the power of 2
b A LaTex expression showing \cos to the power of 2 {(3Pi over 4 )} = 1 + (\frac{square root of 2}{2}) to the power of 2
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 (\frac{\sqrt{2}{2}) to the power of 2 + 1}
b A LaTex expression showing \sin{(7Pi over 4 )} = square root of 1 - (\frac{\sqrt{2}{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{(Pi over 3 )} = square root of (1 over 2 ) to the power of 2 + 1
b A LaTex expression showing \sin{(Pi over 3 )} = square root of 1 - (1 over 2 ) to the power of 2
6
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{(2Pi over 3 )} = square root of 1 - (-1 over 2 ) to the power of 2
b A LaTex expression showing \sin{(2Pi over 3 )} = square root of (-1 over 2 ) to the power of 2 + 1
7
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 3 )} = square root of 1 - (\frac{\sqrt{3}{2}) to the power of 2 }
b A LaTex expression showing \cos{(Pi over 3 )} = square root of (\frac{\sqrt{3}{2}) to the power of 2 + 1}
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 {(5Pi over 6 )} = 1 - (-\frac{square root of 3}{2}) to the power of 2
b A LaTex expression showing \sin to the power of 2 {(5Pi over 6 )} = 1 + (-\frac{square root of 3}{2}) to the power of 2