Trigonometry, Negative Angles Identity (Equations) - Csc/Sec/Cot to Identity (Radians)

Level 1

This math topic focuses on practicing trigonometric identities involving negative angles. It includes evaluating secant, cosecant, and cotangent functions at negative radian measures and determining their relationships with the same trigonometric functions at positive angles. The problems presented encourage understanding of how trigonometric values of negative angles correspond to those of positive angles within the unit circle context. This is introductory material for further exploration of trigonometric identities.

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

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Trigonometry, Negative Angles Identity (Equations) - Csc/Sec/Cot to Identity (Radians) Worksheet

Trigonometry, Negative Angles Identity (Equations) - Csc/Sec/Cot to I...

$A LaTex expression showing \text{sec}(-Pi over 4 )$

What is true about the secant of this negative angle?

a $A LaTex expression showing \text{sec}(-Pi over 4 ) = \text{sec}(Pi over 4 )$

b $A LaTex expression showing \text{sec}(-Pi over 4 ) = -\text{sec}(Pi over 4 )$

$A LaTex expression showing \text{csc}(-Pi over 3 )$

What is true about the cosecant of this negative angle?

a $A LaTex expression showing \text{csc}(-Pi over 3 ) = -\text{csc}(Pi over 3 )$

b $A LaTex expression showing \text{csc}(-Pi over 3 ) = \text{csc}(Pi over 3 )$

$A LaTex expression showing \text{csc}(-Pi over 6 )$

What is true about the cosecant of this negative angle?

a $A LaTex expression showing \text{csc}(-Pi over 6 ) = \text{csc}(Pi over 6 )$

b $A LaTex expression showing \text{csc}(-Pi over 6 ) = -\text{csc}(Pi over 6 )$

$A LaTex expression showing \text{sec}(-2Pi over 3 )$

What is true about the secant of this negative angle?

a $A LaTex expression showing \text{sec}(-2Pi over 3 ) = \text{sec}(2Pi over 3 )$

b $A LaTex expression showing \text{sec}(-2Pi over 3 ) = -\text{sec}(2Pi over 3 )$

$A LaTex expression showing \text{cot}(-3Pi over 4 )$

What is true about the cotangent of this negative angle?

a $A LaTex expression showing \text{cot}(-3Pi over 4 ) = -\text{cot}(3Pi over 4 )$

b $A LaTex expression showing \text{cot}(-3Pi over 4 ) = \text{cot}(3Pi over 4 )$

$A LaTex expression showing \text{csc}(-5Pi over 6 )$

What is true about the cosecant of this negative angle?

a $A LaTex expression showing \text{csc}(-5Pi over 6 ) = \text{csc}(5Pi over 6 )$

b $A LaTex expression showing \text{csc}(-5Pi over 6 ) = -\text{csc}(5Pi over 6 )$

$A LaTex expression showing \text{sec}(-Pi over 6 )$

What is true about the secant of this negative angle?

a $A LaTex expression showing \text{sec}(-Pi over 6 ) = \text{sec}(Pi over 6 )$

b $A LaTex expression showing \text{sec}(-Pi over 6 ) = -\text{sec}(Pi over 6 )$

$A LaTex expression showing \text{cot}(-5Pi over 6 )$

What is true about the cotangent of this negative angle?

a $A LaTex expression showing \text{cot}(-5Pi over 6 ) = \text{cot}(5Pi over 6 )$

b $A LaTex expression showing \text{cot}(-5Pi over 6 ) = -\text{cot}(5Pi over 6 )$