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

 $\cot\theta\sin\theta$  

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• 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!

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