Double and Half Angle Formulas

Use the Half-angle formulas to find the exact value of each expression
sin 22.5º

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

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

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

Tags

CCSS.HSF.TF.C.9

Write the following expression as the sine, cosine, or tangent of an angle.

cos(175)cos(55)+sin(175)sin(55)

a. Sin(120)

b. cos (230)

c. cos (120)

d. sin (230)

• A

• B

• C

• D

Tags

CCSS.HSF.TF.C.9

Use Sum or Difference Identities to find the exact value of each expression.

cos(75°)

• 1/4

• 
• 
• 

Tags

CCSS.HSF.TF.C.9

SIN (105)

• $\sqrt{3}\div2$

• $-\frac{1}{4}\left(\sqrt{2\ }\ +\ \sqrt{6}\right)$

• $\frac{1}{4}\left(\sqrt{2}\ +\ \sqrt{6}\right)$

• 2- $\sqrt{3}$

Tags

CCSS.HSF.TF.C.9

FIND THE EXACT VALUE OF THE EXPRESSION COS(20)COS(40) - SIN(20)SIN(40) 

• 1/4

• 1/2

• $\sqrt{3}$ /2

• $\sqrt{3}$

Tags

CCSS.HSF.TF.C.9

Which of the following is NOT a solution to sin θ = √(3) / 2 ?

• $\frac{\pi}{3}$

• $\frac{2\pi}{3}$

• $\frac{7\pi}{3}$

• $\frac{5\pi}{3}$

Tags

CCSS.HSF.TF.B.7

FIND THE EXACT VALUE OF SIN(105) USING THE HALF ANGLLE IDENTITY.

• $\frac{\left(\sqrt{2\ +\ \sqrt{3}}\right)}{2}$

• $\frac{\left(-\sqrt{3\ +\ \sqrt{2}}\right)}{3}$

• $-\frac{2}{3}$

• $-\sqrt{3}$

Tags

CCSS.HSF.TF.C.9

IN FINDING THE EXACT VALUE OF COS (165) WHICH FROMULA WOULD BE BETTER TO USE?

• SUM

• DIFFERENCE

• HALF ANGLE

• ANY OF THE ABOVE

Tags

CCSS.HSF.TF.C.9