Home
Grade 1Grade 2Grade 3Grade 4Grade 5Grade 6Grade 7Grade 8Grade 9Grade 10Grade 11Grade 12Math Themes
Explorers (Grades 1-3)Explorers Elite (1-3)Navigators (Grades 4-6)Navigators Elite (4-6)Challengers (Grades 7-9)Challengers Elite (7-9)Scholars (Grades 10-12)Scholars Elite (10-12)Schedule an Evaluation
Mobius MethodFlexible ClassesCompanySupport
Pricing
Ctrl+k
Sign InJoin

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

Level 1

This math topic focuses on the application of trigonometric identities within the unit circle, particularly the Pythagorean identity. The questions ask students to utilize the relationships involving sine and cosine functions, specifically their squares under various scenarios, to determine triangle dimensions when angles are given in radians. The problems require students to convert sine and cosine values into their respective squared forms, exploring different mathematical expressions derived from the Pythagorean theorem as used in trigonometry.

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

more
WorksheetView

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

Mobius Math Academy logo
Trigonometry, Unit Circle Pythagorean Identity - Cos/Sin to Identity ...
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{(\gamma)}) to the power of 2 = 1 + (\sin{(\gamma)}) to the power of 2
b A LaTex expression showing (\cos{(\gamma)}) to the power of 2 = 1 - (\sin{(\gamma)}) 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 \cos{(\beta)} = square root of 1 - (\sin{(\beta)) to the power of 2 }
b A LaTex expression showing \cos{(\beta)} = square root of (\sin{(\beta)) to the power of 2 + 1}
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{(\beta)} = square root of (\sin{(\beta)) to the power of 2 + 1}
b A LaTex expression showing \cos{(\beta)} = square root of 1 - (\sin{(\beta)) 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{(\alpha)} = square root of 1 - (\cos{(\alpha)) to the power of 2 }
b A LaTex expression showing \sin{(\alpha)} = square root of (\cos{(\alpha)) to the power of 2 + 1}
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{(\alpha)} = square root of (\sin{(\alpha)) to the power of 2 + 1}
b A LaTex expression showing \cos{(\alpha)} = square root of 1 - (\sin{(\alpha)) 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{(\alpha)} = square root of (\cos{(\alpha)) to the power of 2 + 1}
b A LaTex expression showing \sin{(\alpha)} = square root of 1 - (\cos{(\alpha)) 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 (\cos{(\beta)}) to the power of 2 = 1 + (\sin{(\beta)}) to the power of 2
b A LaTex expression showing (\cos{(\beta)}) to the power of 2 = 1 - (\sin{(\beta)}) to the power of 2
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{(\beta)} = square root of 1 - (\sin{(\beta)) to the power of 2 }
b A LaTex expression showing \cos{(\beta)} = square root of (\sin{(\beta)) to the power of 2 + 1}