Trigonometry Identities - Half Angle to Identity (Greek Letter)

Level 1

This math topic focuses on mastering trigonometric identities, specifically half-angle identities using various Greek letters. Learners engage with expressions for tangent, cosine, and sine of half angles, and they are tasked with completing these identities by choosing the correct formula. The problems feature fundamental trigonometric functions involving half-angles of different variables, testing students' understanding and manipulation of trigonometric concepts in a structured manner.

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 (Greek Letter) Worksheet

Trigonometry Identities - Half Angle to Identity (Greek Letter)

$A LaTex expression showing \text{tan}{(\beta over 2 )}$

Complete the half-angle identity for this expression

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

b $A LaTex expression showing =\pmsquare root of \frac{1+\text{sin(\beta)}{1-\text{sin}(\beta}}$

$A LaTex expression showing \text{cos}{(\gamma over 2 )}$

Complete the half-angle identity for this expression

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

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

$A LaTex expression showing \text{tan}{(\theta over 2 )}$

Complete the half-angle identity for this expression

a $A LaTex expression showing =\frac{\text{sin}(\theta)}{1+\text{cos}(\theta)}$

b $A LaTex expression showing =\frac{1+\text{cos}(\theta)}{1+\text{sin}(\theta)}$

$A LaTex expression showing \text{sin}{(\gamma over 2 )}$

Complete the half-angle identity for this expression

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

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

$A LaTex expression showing \text{sin}{(\theta over 2 )}$

Complete the half-angle identity for this expression

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

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

$A LaTex expression showing \text{cos}{(\alpha over 2 )}$

Complete the half-angle identity for this expression

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

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

$A LaTex expression showing \text{sin}{(\alpha over 2 )}$

Complete the half-angle identity for this expression

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

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

$A LaTex expression showing \text{cos}{(\beta over 2 )}$

Complete the half-angle identity for this expression

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

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