Quiz 5.1 to 5.2 Simplify and Prove Trig Identities

What is the quotient identity for tanθ = ?

• 1/cosθ

• 1/sinθ

• cosθ/sinθ

• sinθ/cosθ

Tags

CCSS.HSF.TF.C.8

What is the reciprocal identity for cscθ= ?

• 1/cosθ

• 1/sinθ

• 1/tanθ

• 1/secθ

Tags

CCSS.HSF.TF.C.8

Simplify

 $\cot\theta\tan\theta$  

Show your work on paper!

• sin²θ/cos²θ

• 1

• 0

• cos²θ/sin²θ

Tags

CCSS.HSF.TF.A.3

Simplify

 $\sin\theta\left(\csc\theta-\sin\theta\right)$  

Show your work on paper!

• secθ

• cos²θ

• sin²θ

• sin²θ/cos²θ

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Simplify

 $\cot\theta\sin\theta$  

Show your work on paper!

• sin²θ

• cosθ

• tanθ

• 1- sin²θ

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Simplify $\left(\sec\theta-1\right)\left(\sec\theta+1\right)$  

Show your work on paper!

• 2secθ

• cot²θ

• tan²θ

• sec²θ + 1

Simplify: tanxcotx-cos²x

Show your work on paper!

• tanx

• cotx

• sin²x

• cos²x

Tags

CCSS.HSA.SSE.A.2

CCSS.HSF.TF.A.3

When this trig identity is simplified what is the final answer?
Trig Identity Given:
 $5+\sin^2x+\cos^2x$  

 our answer in the blank!

(a)  

Tags

CCSS.HSF.TF.C.8

Which two steps can be used to prove the trig identity on the left is equal to the trig identity on the right?

 $\frac{\cos x+\cos x}{\sin x}=2\cot x$ 

• Step 1: Combine cosx + cosx which is  $\cos^2x$  

• Step 1: Combine  cosx + cosx which is  $2\cos x$  

• Step 2: Rewrite  $\frac{\cos x}{\sin x}$  as tanx

• Step 2: Rewrite  $\frac{\cos x}{\sin x}\$  as cotx

Tags

CCSS.HSF.TF.C.9

 $\frac{\sin x}{\cos x}+\frac{\cos x}{\sin x}=\sec x\csc x$  

What 3 steps are used to prove the trig expression on the left is equal to the trig identity on the right?

• Step 1: Cross Multiply cosx and sinx and simplify

• Step 1: Cross Add cosx and sinx and simplify

• Step 2: Rewrite  $\sin^2x+\cos^2x$ using pythgorean identity in the denominator to 1

• Step 2: Rewrite  $\sin^2x+\cos^2x$  using Pythagorean identity in the numerator to 1

• Step 3: Rewrite  $\frac{1}{\sin x\cos x}as\ \sec x\csc x$  using reciprocal identity

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3