Sum/Difference & Double Angle Formulas

Find the exact value of the expression.
 $\sin\left(\frac{5\pi}{12}\right)\cos\left(\frac{\pi}{4}\right)-\cos\left(\frac{5\pi}{12}\right)\sin\left(\frac{\pi}{4}\right)$  

•  $\frac{1}{2}$  

•  $-\frac{1}{2}$  

•  $-\frac{\sqrt{2}}{2}$  

•  $-\frac{\sqrt{3}}{2}$  

Tags

CCSS.HSF.TF.C.9

Given  $\sin\alpha=-\frac{3}{5},\ \cos\alpha=-\frac{4}{5}$   and  $\cos\beta=\frac{2\sqrt{5}}{5},\ \sin\beta=-\frac{\sqrt{5}}{5}$   
Find the exact value of sin (α+β):

• 0

•  $-\frac{2\sqrt{5}}{25}$  

•  $\frac{\sqrt{2}-\sqrt{6}}{4}$  

•  $\frac{\sqrt{8}}{4}$  

Tags

CCSS.HSF.TF.C.9

Given tan α = 3/4 and tan β = (-1/2)

Please find the sum and difference:

tan (α-β)=

• $-\frac{10\sqrt{5}}{25}$

• $-\frac{2\sqrt{5}}{25}$

• $\frac{\sqrt{2}-\sqrt{6}}{4}$

• 2

Tags

CCSS.HSF.TF.C.9

Find the exact value. 
 $\cos\left(265\degree-25\degree\right)$  

•  $\frac{53}{12}$  

•  $-\frac{\sqrt{3}}{2}$  

•  $-\frac{1}{2}$  

•  $\frac{\sqrt{3}}{2}$  

Tags

CCSS.HSF.TF.C.9

Use a sum or difference formula to find an exact value of sin 105º

• $\frac{\sqrt{3}}{2}$

• $\frac{-\sqrt{2}-\sqrt{6}}{4}$

• $\frac{\sqrt{2}+\sqrt{6}}{4}$

• $2-\sqrt{3}$

Tags

CCSS.HSF.TF.C.9

Please select the correct solution

cos ² x + sin ² x=

^{(It's on your reference sheet!!)}

• 1

• csc ² x + sec ² x

• sin ² x

• 1 - sin ² x

Tags

CCSS.HSF.TF.C.8

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

cos θ = 4/5 and 270° < θ < 360°

Find sin 2θ

• $-\frac{1}{5}$

• $\frac{24}{25}$

• $-\frac{24}{25}$

• $-\frac{25}{24}$

Tags

CCSS.HSF.TF.C.9

Find the exact value of  $\sin2x$    if  $\sin x=\frac{12}{13}$   and x is in the first quadrant. 

•  $\frac{120}{169}$  

•  $\frac{25}{169}$  

•  $\frac{60}{169}$  

•  $\frac{5}{13}$  

Tags

CCSS.HSF.TF.C.9

sin2u =

• $\sin u\cos u$

• $2\sin u\cos u$

• $\sin^2u$

• $2\sin^2u$

Tags

CCSS.HSF.TF.C.9

If $\sin\theta=\frac{\sqrt{5}}{3}$  , then  $\cos2\theta$  equals

•  $\frac{1}{3}$  

•  $-\frac{1}{3}$  

•  $\frac{1}{9}$  

•  $-\frac{1}{9}$  

Tags

CCSS.HSF.TF.C.9