4 TRIGNOMETRIC IDENTITIES

Solve the following for cos²θ:
sin²θ + cos²θ = 1

• cos²θ = 1 - sin²θ
• cosθ = 1 + sin²θ
• cosθ = 1 - sinθ
• cos²θ = Adj/hyp

Tags

CCSS.HSF.TF.C.8

Solve the following for tan²θ:
1 + tan²θ = sec²θ 

• tan²θ = sec²θ + 1
• tan²θ = sec²θ - 1
• tanθ = secθ - 1
• tan²θ = opp/adj

Tags

CCSS.HSA.REI.B.4

CCSS.HSF.TF.C.8

Rewrite tan(x) in terms of sin(x) and cos(x).

• tan(x) = cos(x)/sin(x)
• tan(x) = 1/cot(x)
• tan(x) = sin(x)/cos(x)
• tan(x) = opp/adj

Tags

CCSS.HSA.CED.A.4

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

Which expression is equivalent to the trigonometric expression  $\frac{1-\sin^2\left(\theta\right)}{\cos\left(\theta\right)}$  ?

•  $\sec\left(\theta\right)$  

•  $\sin\left(\theta\right)$  

•  $\cos\left(\theta\right)$  

•  $\csc\left(\theta\right)$  

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

•  $\cot\left(\theta\right)$  

•  $\sec\left(\theta\right)$  

•  $\cos\left(\theta\right)$  

•  $\csc\left(\theta\right)$  

Tags

CCSS.HSF.TF.C.8

CCSS.HSG.SRT.C.6

Which expression is equivalent to the trigonometric expression  $\sin\left(\theta\right)\cdot\sec\left(\theta\right)$  ?

•  $\cot\left(\theta\right)$  

•  $1$  

•  $\csc\left(\theta\right)$  

•  $\tan\left(\theta\right)$  

Which expression is equivalent to the trigonometric expression  $\frac{\sin^2\left(\theta\right)+\cos^2\left(\theta\right)}{\sin\left(\theta\right)}$  ?

•  $\sec\left(\theta\right)$  

•  $1$  

•  $\csc\left(\theta\right)$  

•  $\csc^2\left(\theta\right)$  

Tags

CCSS.HSA.SSE.A.2

CCSS.HSA.SSE.B.3

CCSS.HSF.TF.C.8

Is this a pythagorean identity?
tan²x + 1 = secx

• Yes
• No

Tags

CCSS.HSF.TF.C.8

Which of the following is NOT a Pythagorean identity?

• $\tan^2x+1=\sec^2x$

• $\cos2x\ =\ \cos^2x-\sin^2x$

• $\sin^2x\ +\ \cos^2x=1$

• $1+\cot^2x\ =\ \csc^2x$

Tags

CCSS.HSF.TF.C.8

Simplify

 $-\left(\sin^2x+\cos^2x\right)$  

• -1

• 1

• -2

• 2

Tags

CCSS.HSF.TF.C.8