Secant, Cosecant and CotangentA series of free High School Trigonometry Video Lessons from Brightstorm.
Cotangent Graph Cotangent is the reciprocal trig function of tangent function and can be defined as cot(theta)=cos(theta)/sin(theta). It is an odd function, meaning cot(-theta)=-cot(theta), and it has the property that cot(theta+pi)=cot(theta). Because sine is the denominator, and the function is undefined when sin(theta)=0, the cotangent graph has vertical asymptotes at all integer multiples of pi, when sin(theta)=0.
Transforming Secant and Cosecant To graph secant and cosecant, find values of the reciprocal functions and plot them on the coordinate plane. Unlike the graphs of sine and cosine, secant and cosecant have vertical asymptotes whenever the cosine and sine equal zero, respectively. Graphing transformations is made easier by substituting theta for the quantity in parenthesis and solving for x. Also, notice that neither graph has x-intercepts.
Asymptotes of Secant, Cosecant, and Cotangent To find the x-intercepts and asymptotes of secant, cosecant, and cotangent, rewrite them in terms of sine and cosine. Notice that since secant and cosecant have 1 in the numerator and a trig function in the denominator, they can never equal zero; they do not have x-intercepts. The vertical asymptotes of the three functions are whenever the denominators are zero.
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