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

Level 1

This math topic explores trigonometric identities involving the functions tangent (tan) and secant (sec), specifically focusing on identities that connect \( \tan^2 \theta \) and \( \sec^2 \theta \) in degree measure. The problems require converting expressions with \( \tan^2 \theta \) and \( \sec^2 \theta \) to other trigonometric forms using Pythagorean identities. Questions present a trigonometric expression with tan squared or sec squared and ask for completion of the related Pythagorean identity, choosing between potential answers which involve different trigonometric functions.

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 (Degrees) Worksheet

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Trigonometry Identities - Tan^2 and Sec^2 to Identity (Degrees)
1
A LaTex expression showing \text{tan} to the power of 2 {(135 to the power of circle )}
Complete the pythagorean trig identity for this expression
a A LaTex expression showing =\text{sec} to the power of 2 {(135 to the power of circle )} - 1
b A LaTex expression showing =\text{csc} to the power of 2 {(135 to the power of circle )} - 1
2
Complete the pythagorean trig identity for this expression
A LaTex expression showing \text{tan} to the power of 2 {(60 to the power of circle )}
a A LaTex expression showing =\frac{\text{sin} to the power of 2 {(60 to the power of circle )}}{\text{cos} to the power of 2 {(60 to the power of circle )}}
b A LaTex expression showing =\text{sin} to the power of 2 {(60 to the power of circle )} - \text{cos} to the power of 2 {(60 to the power of circle )}
3
A LaTex expression showing \text{tan} to the power of 2 {(120 to the power of circle )}
Complete the pythagorean trig identity for this expression
a A LaTex expression showing =1 - \text{sec} to the power of 2 {(120 to the power of circle )}
b A LaTex expression showing =\text{sec} to the power of 2 {(120 to the power of circle )} - 1
4
A LaTex expression showing \text{cos} to the power of 2 {(240 to the power of circle )}
Complete the pythagorean trig identity for this expression
a A LaTex expression showing =\frac{\text{tan} to the power of 2 {(240 to the power of circle )}}{\text{sin} to the power of 2 {(240 to the power of circle )}}
b A LaTex expression showing =\frac{\text{sin} to the power of 2 {(240 to the power of circle )}}{\text{tan} to the power of 2 {(240 to the power of circle )}}
5
A LaTex expression showing \text{cos} to the power of 2 {(60 to the power of circle )}
Complete the pythagorean trig identity for this expression
a A LaTex expression showing =\frac{\text{tan} to the power of 2 {(60 to the power of circle )}}{\text{sin} to the power of 2 {(60 to the power of circle )}}
b A LaTex expression showing =\frac{\text{sin} to the power of 2 {(60 to the power of circle )}}{\text{tan} to the power of 2 {(60 to the power of circle )}}
6
Complete the pythagorean trig identity for this expression
A LaTex expression showing \text{sec} to the power of 2 {(120 to the power of circle )}
a A LaTex expression showing =\text{tan} to the power of 2 {(120 to the power of circle )} + 1
b A LaTex expression showing =1 - \text{tan} to the power of 2 {(120 to the power of circle )}
7
Complete the pythagorean trig identity for this expression
A LaTex expression showing \text{tan} to the power of 2 {(45 to the power of circle )}
a A LaTex expression showing =\text{sin} to the power of 2 {(45 to the power of circle )} - \text{cos} to the power of 2 {(45 to the power of circle )}
b A LaTex expression showing =\frac{\text{sin} to the power of 2 {(45 to the power of circle )}}{\text{cos} to the power of 2 {(45 to the power of circle )}}
8
Complete the pythagorean trig identity for this expression
A LaTex expression showing \text{sin} to the power of 2 {(150 to the power of circle )}
a A LaTex expression showing =\text{tan} to the power of 2 {(150 to the power of circle )} times \text{cos} to the power of 2 {(150 to the power of circle )}
b A LaTex expression showing =\text{tan} to the power of 2 {(150 to the power of circle )} - \text{cos} to the power of 2 {(150 to the power of circle )}