Trigonometry Identities - Half Angle to Identity (Radians)

Level 1

This topic focuses on practicing half-angle trigonometric identities using radians. It is designed as an introductory exploration into trigonometric identities. Participants are required to complete expressions involving half-angle identities of sine, cosine, and tangent functions at specific radian measures. Each problem presents a trigonometric function at a half angle and asks the learner to determine the corrected identity using multiple-choice answers. The questions address understanding and manipulation of fundamental trigonometric identities, enhancing the learners' ability to work with angles and trigonometry in radians.

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

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Trigonometry Identities - Half Angle to Identity (Radians) Worksheet

Trigonometry Identities - Half Angle to Identity (Radians)

$A LaTex expression showing \text{sin}{(\frac{2Pi over 3 }{2})}$

Complete the half-angle identity for this expression

a $A LaTex expression showing =\pmsquare root of \frac{1-\text{cos(2Pi over 3 )}{2}}$

b $A LaTex expression showing =\pmsquare root of \frac{1+\text{cos(2Pi over 3 )}{2}}$

$A LaTex expression showing \text{tan}{(\frac{3Pi over 4 }{2})}$

Complete the half-angle identity for this expression

a $A LaTex expression showing =\pmsquare root of \frac{1+\text{sin(3Pi over 4 )}{2}}$

b $A LaTex expression showing =\pmsquare root of \frac{1-\text{cos(3Pi over 4 )}{1+\text{cos}(3Pi over 4 )}}$

$A LaTex expression showing \text{cos}{(\frac{Pi over 3 }{2})}$

Complete the half-angle identity for this expression

a $A LaTex expression showing =\pmsquare root of \frac{1+\text{cos(Pi over 3 )}{2}}$

b $A LaTex expression showing =\pmsquare root of \frac{1+\text{cos(Pi over 3 )}{1-\text{cos}(Pi over 3 }}$

$A LaTex expression showing \text{tan}{(\frac{Pi over 6 }{2})}$

Complete the half-angle identity for this expression

a $A LaTex expression showing =\pmsquare root of \frac{1-\text{cos(Pi over 6 )}{1+\text{cos}(Pi over 6 )}}$

b $A LaTex expression showing =\pmsquare root of \frac{1+\text{sin(Pi over 6 )}{2}}$

$A LaTex expression showing \text{sin}{(\frac{7Pi over 6 }{2})}$

Complete the half-angle identity for this expression

a $A LaTex expression showing =\pmsquare root of \frac{1+\text{cos(7Pi over 6 )}{1-\text{cos}(7Pi over 6 }}$

b $A LaTex expression showing =\pmsquare root of \frac{1-\text{cos(7Pi over 6 )}{2}}$

$A LaTex expression showing \text{sin}{(\frac{11Pi over 6 }{2})}$

Complete the half-angle identity for this expression

a $A LaTex expression showing =\pmsquare root of \frac{1+\text{cos(11Pi over 6 )}{2}}$

b $A LaTex expression showing =\pmsquare root of \frac{1-\text{cos(11Pi over 6 )}{2}}$

$A LaTex expression showing \text{sin}{(\frac{5Pi over 4 }{2})}$

Complete the half-angle identity for this expression

a $A LaTex expression showing =\pmsquare root of \frac{1-\text{cos(5Pi over 4 )}{2}}$

b $A LaTex expression showing =\pmsquare root of \frac{1+\text{cos(5Pi over 4 )}{1-\text{cos}(5Pi over 4 }}$

$A LaTex expression showing \text{sin}{(\frac{Pi over 4 }{2})}$

Complete the half-angle identity for this expression

a $A LaTex expression showing =\pmsquare root of \frac{1+\text{cos(Pi over 4 )}{2}}$

b $A LaTex expression showing =\pmsquare root of \frac{1-\text{cos(Pi over 4 )}{2}}$