Tangent, Cotangent, Secant, Cosecant Functions

4-5 Tan, Cot, Csc, Sec Graphs

Multiple Choice

$$\cos\left(\frac{5\pi}{6}\right)=$$  

• $$\frac{\sqrt[]{3}}{2}$$  

• 1/2

• $$-\ \frac{\sqrt[]{3}}{2}$$  

• - 1/2

Multiple Choice

$$\cot\left(\frac{3\pi}{2}\right)=$$  

• undefined

• - 1

• 1

• 0

Multiple Choice

$$\csc\left(\frac{4\pi}{3}\right)=$$  

• 2

• $$-\ \frac{2\ \sqrt[]{3}}{3}$$  

• $$\frac{2\ \sqrt[]{3}}{3}$$  

• -2

Draw

Sketch the graph of y=cosx.

Multiple Choice

What is the reciprocal of cosine?

• Cosecant

• Secant

• Tangent

• Cotangent

• Sine

Draw

Sketch the graph of y=secx.

Draw

Sketch the graph of y=sinx.

Multiple Choice

What is the reciprocal of sine?

• Cosecant

• Secant

• Tangent

• Cotangent

• Sine

Draw

Sketch the graph of y=cscx.

Multiple Choice

Find the period of $$f\left(x\right)=3\csc\left(\frac{\pi}{4}x\right)$$  .

• $$\frac{\pi}{2}$$  

• 1/2

• $$8\pi$$  

• 8

Multiple Choice

Find the phase shift of $$f\left(x\right)=\frac{1}{2}\sec\left(2x-5\pi\right)+1$$  .

• $$-\frac{5\pi}{2}$$  

  (left)

• 5

  (right)

• $$\frac{5\pi}{2}$$

  (right) 

• -5

  (left)

Multiple Select

Select all equivalent expressions of $$\tan\theta$$  .

• $$\frac{\sin\theta}{\cos\theta}$$  

•  y/x

• $$\frac{\cos\theta}{\sin\theta}$$  

•  x/y

• $$\frac{1}{\sec\theta}$$  

Multiple Select

Where is tangent undefined on the unit circle? Select all that apply.

• $$\frac{3\pi}{2}$$  

• $$0\pi$$  

• $$2\pi$$  

• $$\frac{\pi}{2}$$  

• $$\pi$$  

Multiple Select

Where is tangent equal to 0 on the unit circle? Select all that apply.

• $$\frac{3\pi}{2}$$  

• $$0\pi$$  

• $$2\pi$$  

• $$\frac{\pi}{2}$$  

• $$\pi$$  

Multiple Choice

What are the vertical asymptotes of the tangent parent function?

• ALL multiples of $$\pm\pi$$  

• ALL multiples of $$\pm\frac{\pi}{2}$$  

• ODD multiples of $$\pm\frac{\pi}{2}$$  

• ODD multiples of $$\pm\pi$$  

Multiple Choice

Where are the zeros of the tangent parent function?

• ALL multiples of $$\pm\pi$$  

• ALL multiples of $$\pm\frac{\pi}{2}$$  

• ODD multiples of $$\pm\frac{\pi}{2}$$  

• ODD multiples of $$\pm\pi$$  

Draw

Sketch the graph of y=tanx.

Multiple Select

Select all equivalent expressions of $$\cot\theta$$  .

• $$\frac{\sin\theta}{\cos\theta}$$  

•  y/x

• $$\frac{\cos\theta}{\sin\theta}$$  

•  x/y

• $$\frac{1}{\sec\theta}$$  

Multiple Select

Where is cotangent undefined on the unit circle? Select all that apply.

• $$\frac{3\pi}{2}$$  

• $$0\pi$$  

• $$2\pi$$  

• $$\frac{\pi}{2}$$  

• $$\pi$$  

Multiple Select

Where is cotangent equal to 0 on the unit circle? Select all that apply.

• $$\frac{3\pi}{2}$$  

• $$0\pi$$  

• $$2\pi$$  

• $$\frac{\pi}{2}$$  

• $$\pi$$  

Multiple Choice

What are the vertical asymptotes of the cotangent parent function?

• ALL multiples of $$\pm\pi$$  

• ALL multiples of $$\pm\frac{\pi}{2}$$  

• ODD multiples of $$\pm\frac{\pi}{2}$$  

• ODD multiples of $$\pm\pi$$  

Multiple Choice

Where are the zeros of the cotangent parent function?

• ALL multiples of $$\pm\pi$$  

• ALL multiples of $$\pm\frac{\pi}{2}$$  

• ODD multiples of $$\pm\frac{\pi}{2}$$  

• ODD multiples of $$\pm\pi$$  

Draw

Sketch the graph of cotangent.

Multiple Choice

Find the period of $$y=\frac{1}{3}\tan\left(3x\right)+2$$  

• $$\frac{2\pi}{3}$$  

• $$\frac{\pi}{3}$$  

• 2/3

• 1/3

• 3

Multiple Choice

Find the period of $$y=-\cot\left(4\pi x-1\right)$$  

• $$\frac{\pi}{2}$$  

• $$\frac{\pi}{4}$$  

• 1/4

• 1/2

• $$4\pi$$  

Multiple Choice

Find the phase shift of $$y=-\cot\left(4\pi x-1\right)$$  

• $$\frac{\pi}{4}$$  

  (right)

• $$\frac{1}{4\pi}$$  

  (right)

• 1/4

  (right)

• 1

  (right)

• $$-4\pi$$  

  (left)