Basic trig functions important facts

What is the shape and key characteristics of the graph of y=sin⁡(x)?

• The graph is a smooth, periodic wave oscillating between -1 and 1.

• Period: 2π

• Amplitude: 1

• Phase shift: None

• Key Points:

  • sin⁡(0)=0

  • sin⁡(π/2)=1

  • sin⁡(π)=0

  • sin⁡(3π/2)=−1

  • sin⁡(2π)=0

What is the shape and key characteristics of the graph of y=cos⁡(x)?

• Period: 2π

• Amplitude: 1

• Phase shift: None

• Key Points:

  • cos⁡(0)=1

  • cos⁡(π/2)==0

  • cos⁡(π)=−1

  • cos⁡(3π/2)=0

  • cos⁡(2π)=1

What is the shape and key characteristics of the graph of y=tan⁡(x)

• The graph consists of repeating curves with vertical asymptotes where cos⁡(x)=0, x-pi/2, x=3pi/2, etc

• Period: π

• Amplitude: No maximum or minimum (goes to ∞ and −∞)

• Key Points:

  • tan⁡(0)=0

  • tan⁡(π/4)=1

  • tan⁡(−π/4)=−1

  • Asymptotes at x=±π/2

What is the shape and key characteristics of the graph of y=csc⁡(x)

• The graph is a series of U-shaped curves with vertical asymptotes where sin⁡(x)=0 at x=0, x= +pi, +-2pi…)

• Period: 2π

• Amplitude: No maximum or minimum (goes to ∞ and −∞-and −∞)

• Key Points:

  • Asymptotes at x=0,±π,,±2π

  • Peaks at x=+pi/2, +-3pi/2…)

What is the shape and key characteristics of the graph of y=sec⁡(x)?

• The graph consists of U-shaped curves with vertical asymptotes where cos⁡(x)=0\ at x=±π/2,±3π/2,…

• Period: 2π

• Amplitude: No maximum or minimum (goes to ∞and −∞-and −∞)

• Key Points:

  • Asymptotes at x=±π/2,±3π/2x

  • Peaks at x=0,±π,±2π,…

What is the shape and key characteristics of y=cot(x)?

The graph consists of repeating curves with vertical asymptotes where sin⁡(x)= 0 at x=0,±π,±2π,…

Period- pi

Amplitude- no max or min, goes to positive and negative infinity

Key points:

-cot(0) is undefined

-cot(pi/4)=1.

-Asymptotes at x=0 ,pi, ,±2pi, …