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Half Angle, Double Angle, Sum/Difference Concepts

Total questions: 10

Worksheet time: 23mins

Name
Class
Date
1.

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

a)

Positive

b)

Negative

c)

Positive or negative

d)

Undefined

2.

 The terminal side of an angle β\beta is located in Quadrant IV and
 0°<β<360°0\degree<\beta<360\degree  
  tan⁡(β2)\tan\left(\frac{\beta}{2}\right)  must be:

a)

Positive

b)

Negative

c)

Can't tell 

d)

Could be positive or negative

3.

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


a)

The double angle formula

b)

The half angle formula

c)

A sum/difference formula

d)

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

4.

Choose all appropriate answers:

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

a)

A good strategy to use if you have the time

b)

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

c)

not necessary because your calculator gives exact values

d)

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

5.

In the expression: 3−sin⁡x3+cos⁡x\frac{3-\sin x}{3+\cos x}  
the 3s can be cancelled from the numerator and denominator.

a)

True

b)

False

6.

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

a)

 105°105\degree  

b)

 15°15\degree  

c)

 165°165\degree  

d)

 10°10\degree  

7.

 2+3\sqrt{2}+\sqrt{3}  is equal to

a)

 5\sqrt{5}  

b)

 6\sqrt{6}  

c)

Can't be simplified

d)

 3.14626433.1462643  

8.

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

If  0°<α<360°0\degree<\alpha<360\degree  

then  cos⁡(α2)\cos\left(\frac{\alpha}{2}\right)  must be:

a)

Positive

b)

Negative

c)

Can't tell 

d)

Could be positive or negative

9.

 Choose all correct answers: If the terminal side of an angle θ\theta is located in Quadrant I, then  sin⁡(θ2)\sin\left(\frac{\theta}{2}\right)  could be:

a)

Positive if  0°<θ<90°0\degree<\theta<90\degree  

b)

Negative if  360°<θ<450°360\degree<\theta<450\degree  

c)

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

d)

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

10.

Rewrite the angle 5π8\frac{5\pi}{8}  as if you were going to use the half angle formula.

a)

 5π4\frac{5\pi}{4}  

b)

 5π42\frac{\frac{5\pi}{4}}{2}  

c)

 10π8\frac{10\pi}{8}  

d)

 22.5°22.5\degree