Trigonometry, Unit Circle Pythagorean Identity - X,Y to X,Y Identity

Level 1

This math topic focuses on practicing trigonometry and the unit circle, specifically using the Pythagorean identity to determine X and Y dimensions of triangles within the unit circle. The questions involve applying the Pythagorean theorem in various ways to solve for either the X or Y component of a point on the unit circle, based on given values or expressions. Each question provides two potential answers, requiring students to choose or compute the correct one based on their understanding of the relationships between the sides of a right triangle in the context of trigonometry.

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

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Trigonometry, Unit Circle Pythagorean Identity - X,Y to X,Y Identity Worksheet

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Trigonometry, Unit Circle Pythagorean Identity - X,Y to X,Y 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 y to the power of 2 = 1 + x to the power of 2
b A LaTex expression showing y to the power of 2 = 1 - x to the power of 2
2
An svg image showing a math problem
What does Pythagoras tell us about the X dimension of this triangle?
a A LaTex expression showing x = square root of 1 - y to the power of 2
b A LaTex expression showing x = square root of y to the power of 2 + 1
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 y = square root of x to the power of 2 + 1
b A LaTex expression showing y = square root of 1 - x 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 y = square root of x to the power of 2 + 1
b A LaTex expression showing y = square root of 1 - x to the power of 2
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 x = square root of 1 - y to the power of 2
b A LaTex expression showing x = square root of y to the power of 2 + 1
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 x to the power of 2 = 1 - y to the power of 2
b A LaTex expression showing x to the power of 2 = 1 + y to the power of 2
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 x to the power of 2 = 1 - y to the power of 2
b A LaTex expression showing x to the power of 2 = 1 + y 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 y = square root of 1 - x to the power of 2
b A LaTex expression showing y = square root of x to the power of 2 + 1