Double- and Half-Angle Identities

 $\cos70^o\cos40^o-\sin70^o\sin40^o\$  is equivalent to

•  $\cos30^o$  

•  $\cos70^{o\ }$  

•  $\cos110^o$  

•  $\sin70^{o\ }$  

Tags

CCSS.HSF.TF.C.9

If  $\sin A=\frac{3}{5},\sin B=\frac{2}{3},$   $and\ \angle A\ and\ \angle B$  are acute angles, what is the value of  $\cos\left(A-B\right)?$  

•  $-\frac{2}{3}$  

•  $\frac{4\sqrt{5}-6}{15}$  

•  $\frac{4\sqrt{5}+2}{5}$  

•  $\frac{4\sqrt{5}+6}{15}$  

Tags

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.9

Use the information about the angle θ, 0≤θ<2π to find the exact value of 
sin (θ/2)
2. sin θ= 3/5 , 0<θ<π/2

• √10/10
• 24/25
• 25/7
• -7/25

Tags

CCSS.HSF.TF.C.9

Use the information about the angle θ, 0≤θ<2π to find the exact value of 
tan (θ/2)
3. tanθ=4/3, π<θ<3π/2

• -2
• 4/5
• -24/7
• 1/2

Tags

CCSS.HSF.TF.C.9

Use the Half-angle formulas to find the exact value of each expression
cos 165º

• -√(2+√3)/2
• -√(2-√3)/2
• √(2+√3)/2
• √(2-√3)/2

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.9

Use a double-angle or half-angle identity to find the exact value of each expression
sin θ = −3/5 and 3π/2 < θ < 2π Find tan θ/2

• -1/3
• -√3
• √3/3
• -1

Tags

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

If cosx = - 4/5, find secx.

• -5/4

• -3/5

• 5/3

• √3/2

Tags

CCSS.HSF.TF.C.8