Double Angles

cos2u =

• $2\sin u\cos u$

• $\cos^2u-\sin^2u$

• $2\cos^2u-2$

• $\sin^2u-\cos^2u$

Which identity represents a double-angle identity for sin 2θ?

• 2sinθcosθ
• cos²θ - sin²θ
• 1 - 2sin²θ
• 2cos²θ - 1

Tags

CCSS.HSF.TF.C.9

Use a double-angle or half-angle identity to find the exact value of each expression

cos θ = 4/5 and 270° < θ < 360°Find sin 2θ

• -1/5

• 24/25

• -24/25

• -25/24

Tags

CCSS.HSF.TF.C.8

CCSS.HSF.TF.C.9

Find the exact value of sin 2x if sin x = 12/13 and x is in the first quadrant. 

• 120/169
• 25/169
• 60/169
• 5/13

Tags

CCSS.HSF.TF.C.8

CCSS.HSF.TF.C.9

If cosx = - 4/5, find secx.

• -5/4

• -3/5

• 5/3

• √3/2

Tags

CCSS.HSF.TF.C.8

CCSS.HSG.SRT.C.8

 $Given\ \cos\theta=\frac{5}{13}\ and\ \frac{3\pi}{2}<\theta<2\pi\ find\ \sin2\theta$  

•  $\frac{120}{169}$  

•  $-\frac{120}{169}$  

•  $\frac{24}{26}$  

•  $\frac{10}{26}$  

Given that $\sin\theta=\frac{3}{7}\ where\ \frac{\pi}{2}<\theta<\pi,\ \ find\ \cos2\theta$  

•  $-\frac{31}{49}$  

•  $\frac{11}{49}$  

•  $-\frac{11}{49}$  

•  $\frac{31}{49}$  

 $Given\ \cos x=\frac{5}{13\ }\ where\ x\ is\ in\ Quadrant\ 1,\ find\ \tan2\theta$  

•  $-\frac{119}{120}$  

•  $-\frac{120}{119}$  

•  $\frac{119}{120}$  

•  $\frac{120}{119}$  

 $Given\ \sin\alpha=\frac{3}{7}\ and\ \theta\ is\ in\ Quadrant\ 2,\ find\ \sin2\theta$  

•  $-\frac{12\sqrt{10}}{49}$  

•  $-\frac{6\sqrt{40}}{49}$  

•  $\frac{12\sqrt{10}}{49}$  

•  $\frac{6\sqrt{40}}{49}$  

 $Given\ \sin\beta=-\frac{5}{8}\ where\ 270\degree<\beta<360\degree,\ find\ \tan2\beta$  

•  $-\frac{8}{5}$  

•  $\frac{5\sqrt{39}}{7}$  

•  $-\frac{5\sqrt{39}}{7}$  

• -4.46