BQ#3 – Unit T Concepts 1-3

• How do the graphs of sine and cosine relate to each of the others?  Emphasize asymptotes in your response.

Tangent?

Tangent is equal to sin/cos. It is undefined when cos=0. When sin=0, tangent goes through the x-axis since tan=0.

Cotangent?

Cotangent is equalled to cos/sin. In Quadrant 1, t will be positive since the sin and cos graphs are positive. If the sin=1, cotangent will have asymptotes. In Quadrant 2, cos is negative; sin is positive. In quadrant 3, cos is negative; sin is negative. Their signs cancel out to make a positive cotangent. In Quadrant 4, cos is positive; sin is negative. This will give cotangent a negative answer.

Secant?

The reciprocal of secant is 1/cos. If cos=0, sec is undefined and will not touch. However, if the cos=1, sec amplitudes will touch.

Cosecant?

The reciprocal of cosecant is 1/sin. If sin=0, cosecant is undefined and will not touch. However, if sin=1, csc amplitudes will touch.