Half Angle, Double Angle, Sum/Difference Concepts

If the terminal side of an angle  $\theta$  is located in QI, then  $\cos\left(2\theta\right)$  will be:

• Positive

• Negative

• Positive or negative

• Undefined

 The terminal side of an angle $\beta$ is located in Quadrant IV and
 $0\degree<\beta<360\degree$  
  $\tan\left(\frac{\beta}{2}\right)$  must be:

• Positive

• Negative

• Can't tell 

• Could be positive or negative

To find an exact value for the expression: $\sin\left(67.5\degree\right)$  , you should use 

• The double angle formula

• The half angle formula

• A sum/difference formula

• Just put it in your calculator because it gives you exact answers.

Choose all appropriate answers:

Using your calculator to double check that your exact value is correct is

• A good strategy to use if you have the time

• time well spent as long as you're careful when entering your expression

• not necessary because your calculator gives exact values

• a nice trick to helping you find out if you made any little mistakes along the way

In the expression: $\frac{3-\sin x}{3+\cos x}$  
the 3s can be cancelled from the numerator and denominator.

• True

• False

Which angle measure can't be evaluated using a trig function with the sum/difference formula?

•  $105\degree$  

•  $15\degree$  

•  $165\degree$  

•  $10\degree$  

 $\sqrt{2}+\sqrt{3}$  is equal to

•  $\sqrt{5}$  

•  $\sqrt{6}$  

• Can't be simplified

•  $3.1462643$  

The terminal side of an angle $\alpha$ is located in Quadrant III. 

If  $0\degree<\alpha<360\degree$  

then  $\cos\left(\frac{\alpha}{2}\right)$  must be:

• Positive

• Negative

• Can't tell 

• Could be positive or negative

 Choose all correct answers: If the terminal side of an angle $\theta$ is located in Quadrant I, then  $\sin\left(\frac{\theta}{2}\right)$  could be:

• Positive if  $0\degree<\theta<90\degree$  

• Negative if  $360\degree<\theta<450\degree$  

• Negative if  $0\degree<\theta<90\degree$  

• Positive if  $360\degree<\theta<450\degree$  

Rewrite the angle $\frac{5\pi}{8}$  as if you were going to use the half angle formula.

•  $\frac{5\pi}{4}$  

•  $\frac{\frac{5\pi}{4}}{2}$  

•  $\frac{10\pi}{8}$  

•  $22.5\degree$