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Trigonometry Identities - Tan^2 and Sec^2 to Identity (Radians)

Level 1

This math topic focuses on practicing trigonometric identities involving the functions tangent (tan) and secant (sec) squared, particularly transforming these expressions to other trigonometric forms. The problems are presented in a multiple-choice answer format where learners must complete Pythagorean identities based on given trigonometric expressions involving angles in radians. These problems are foundational for understanding relationships between different trigonometric functions and are part of an introductory unit on trigonometric identities. The exercises require manipulating these identities to arrive at the correct transformations and simplifications.

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

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Trigonometry Identities - Tan^2 and Sec^2 to Identity (Radians) Worksheet

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Trigonometry Identities - Tan^2 and Sec^2 to Identity (Radians)
1
A LaTex expression showing \text{tan} to the power of 2 {(Pi over 4 )}
Complete the pythagorean trig identity for this expression
a A LaTex expression showing =\text{sin} to the power of 2 {(Pi over 4 )} - \text{cos} to the power of 2 {(Pi over 4 )}
b A LaTex expression showing =\frac{\text{sin} to the power of 2 {(Pi over 4 )}}{\text{cos} to the power of 2 {(Pi over 4 )}}
2
A LaTex expression showing \text{cos} to the power of 2 {(5Pi over 3 )}
Complete the pythagorean trig identity for this expression
a A LaTex expression showing =\frac{\text{sin} to the power of 2 {(5Pi over 3 )}}{\text{tan} to the power of 2 {(5Pi over 3 )}}
b A LaTex expression showing =\frac{\text{tan} to the power of 2 {(5Pi over 3 )}}{\text{sin} to the power of 2 {(5Pi over 3 )}}
3
A LaTex expression showing \text{cos} to the power of 2 {(5Pi over 6 )}
Complete the pythagorean trig identity for this expression
a A LaTex expression showing =\frac{\text{sin} to the power of 2 {(5Pi over 6 )}}{\text{tan} to the power of 2 {(5Pi over 6 )}}
b A LaTex expression showing =\frac{\text{tan} to the power of 2 {(5Pi over 6 )}}{\text{sin} to the power of 2 {(5Pi over 6 )}}
4
A LaTex expression showing \text{sin} to the power of 2 {(7Pi over 6 )}
Complete the pythagorean trig identity for this expression
a A LaTex expression showing =\frac{\text{cos} to the power of 2 {(7Pi over 6 )}}{\text{tan} to the power of 2 {(7Pi over 6 )}}
b A LaTex expression showing =\text{tan} to the power of 2 {(7Pi over 6 )} times \text{cos} to the power of 2 {(7Pi over 6 )}
5
A LaTex expression showing \text{sec} to the power of 2 {(7Pi over 4 )}
Complete the pythagorean trig identity for this expression
a A LaTex expression showing =\text{tan} to the power of 2 {(7Pi over 4 )} + 1
b A LaTex expression showing =\text{tan} to the power of 2 {(7Pi over 4 )} - 1
6
A LaTex expression showing \text{cos} to the power of 2 {(5Pi over 4 )}
Complete the pythagorean trig identity for this expression
a A LaTex expression showing =\frac{\text{tan} to the power of 2 {(5Pi over 4 )}}{\text{sin} to the power of 2 {(5Pi over 4 )}}
b A LaTex expression showing =\frac{\text{sin} to the power of 2 {(5Pi over 4 )}}{\text{tan} to the power of 2 {(5Pi over 4 )}}
7
A LaTex expression showing \text{sec} to the power of 2 {(5Pi over 4 )}
Complete the pythagorean trig identity for this expression
a A LaTex expression showing =\text{tan} to the power of 2 {(5Pi over 4 )} - 1
b A LaTex expression showing =\text{tan} to the power of 2 {(5Pi over 4 )} + 1
8
A LaTex expression showing \text{sec} to the power of 2 {(5Pi over 6 )}
Complete the pythagorean trig identity for this expression
a A LaTex expression showing =\text{tan} to the power of 2 {(5Pi over 6 )} + 1
b A LaTex expression showing =\text{tan} to the power of 2 {(5Pi over 6 )} - 1