Double Angle Identities

 $\cot\left(\theta\right)=-\frac{4}{3}$  and  $270\degree<\theta<360\degree$ . Find  $\sec\left(2\theta\right)$  

•  $-\frac{25}{24}$  

•  $\frac{25}{24}$  

•  $\frac{7}{24}$  

•  $\frac{25}{7}$  

Tags

CCSS.HSF.TF.C.9

 $\csc\theta=-\frac{\sqrt{13}}{2}$  and  $\pi<\theta<\frac{3\pi}{2}$ . Find  $\tan2\theta$  

•  $\frac{401\sqrt{465}}{7440}$  

•  $\frac{5}{12}$  

•  $\frac{7}{24}$  

•  $\frac{12}{5}$  

Tags

CCSS.HSF.TF.C.9

Write as a single trig function of a single angle.
 $2\sin\frac{\pi}{5}\cos\frac{\pi}{5}$  

•  $\sin\frac{\pi}{10}$  

•  $\sin\frac{2\pi}{5}$  

•  $\cos\frac{2\pi}{5}$  

•  $\cos\frac{\pi}{10}$  

Tags

CCSS.HSF.TF.C.9

Write as a single trig function of a single angle:
 $\cos^232\degree-\sin^232\degree$  

•  $\cos64\degree$  

•  $\cos16\degree$  

•  $\sin64\degree$  

•  $\sin16\degree$  

Tags

CCSS.HSF.TF.C.8

Use a double angle identity to find the exact value of 
 $\sin420\degree$  

•  $-1$  

• 0

•  $\frac{1}{2}$  

•  $\frac{\sqrt{3}}{2}$  

Tags

CCSS.HSF.TF.C.9

Simplify:

 $\frac{1-\cos2x}{2}$ 

•  $-\sin^2x$  

•  $\sin^2x$  

•  $0$  

•  $\cos^2x$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.TF.C.8

Write as a single trig function of a single angle:
 $\frac{2\tan140\degree}{1-\tan^2140\degree}$  

•  $\tan140\degree$  

•  $\tan70\degree$  

•  $\tan280\degree$  

•  $\cot280\degree$  

Tags

CCSS.HSF.TF.C.9

Use a double angle identity to find the exact value of 
 $\cos450\degree$  

•  $-1$  

• 0

•  $\frac{1}{2}$  

•  $\frac{\sqrt{3}}{2}$  

Tags

CCSS.HSF.TF.C.9

Use a double angle identity to find the exact value of 
 $\tan480\degree$  

•  $-\sqrt{3}$  

•  $\sqrt{3}$  

•  $\frac{\sqrt{3}}{3}$  

•  $-\frac{\sqrt{3}}{3}$  

Tags

CCSS.HSF.TF.C.9

 $\cos\theta=\frac{4}{5}\ \ and\ \ \frac{3\pi}{2}<\theta<2\pi$  

Find the exact value of  $\sin2\theta$ .

•  $-\frac{1}{5}$   

•  $\frac{24}{25}$  

•  $-\frac{24}{25}$  

•  $-\frac{25}{24}$  

Tags

CCSS.HSF.TF.C.9