Applying and analysing trigonometric functions

Simplify (Hint: you will need to FOIL first)

• sinθ

• cot²θ

• tan²θ

• cos²θ

Which expression is equivalent to the trigonometric expression  $\frac{\tan\left(\theta\right)}{\sin\left(\theta\right)}$  ?

•  $\cot\left(\theta\right)$  

•  $\sec\left(\theta\right)$  

•  $\cos\left(\theta\right)$  

•  $\csc\left(\theta\right)$  

Simplify.

• sinθ
• cos²θ
• sin²θ
• 1- sin²θ

True or False: We can check identities

• True

• False

• True 

• False 

(csc²(θ))(1 - cos²(θ))

• A. sec(θ)

• B. 1

• C. -1

• D. -sin(θ)

Cot²x - cosec²x =

• 1

• 2

• -1

• 0

Simplify:  $\secθ\sinθ$  

• cos θ

• csc θ

• tan θ

• cot θ

 $\frac{\cos^2\theta}{\sin^2\theta}+\csc\theta\cdot\sin\theta$  

•  $\csc^2\theta$  

•  $\tan^2\theta$  

•  $\sec^2\theta$  

•  $1$  

Simplify:  $\sin\left(\frac{x}{2}\right)\cos\left(\frac{x}{2}\right)$  

•  $\cos x$  

•  $\frac{\cos x}{2}$  

•  $\sin x$  

•  $\frac{\sin x}{2}$