Sine Graph Cosine Graph
Period: 2pi Period: 2pi
Amplitude: 1 Amplitude: 1
Period: 2pi Period: 2pi
Amplitude: 1 Amplitude: 1
Tan Graph Sec Graph
Period: pi Period: pi/2
Amplitude: Infinity Amplitude: infinity
Period: pi Period: pi/2
Amplitude: Infinity Amplitude: infinity
Csc Graph Cot Graph
Period: 2pi Period: pi
Amplitude: Infinity Amplitude: Infinity
Period: 2pi Period: pi
Amplitude: Infinity Amplitude: Infinity
Comparing Sine and Cosine
Sine and cosine graphs are the same except for where they start on the y-axis. Sine graphs start at (0,0) and the cosine graphs start at whatever the amplitude is.
Vertical Asymptotes
The vertical asymptotes for sec, csc, and cot are where they are because of their reciprocals. Sec is 1/cos so whenever cosine is equal to 0, there's an asymptote. Csc is 1/sin so whenever sine is equal to 0, there's an asymptote. Cot is 1/tan so whenever tangent is equal to 0, there's an asymptote. For tangent, it equals sin/cos so when cosine is 0, there's an asymptote.
Sine and cosine graphs are the same except for where they start on the y-axis. Sine graphs start at (0,0) and the cosine graphs start at whatever the amplitude is.
Vertical Asymptotes
The vertical asymptotes for sec, csc, and cot are where they are because of their reciprocals. Sec is 1/cos so whenever cosine is equal to 0, there's an asymptote. Csc is 1/sin so whenever sine is equal to 0, there's an asymptote. Cot is 1/tan so whenever tangent is equal to 0, there's an asymptote. For tangent, it equals sin/cos so when cosine is 0, there's an asymptote.