Tangent
The graph above shows a picture that has a sine, cosine, and tangent graph all in one. We know that sine is positive in the 1st and 2nd quadrants while cosine is positive in the 1st and 4th quadrants. Apart from this, we also know that the trig ratio for tangent is sine/cosine. So in that case, if both sine and cosine are positive, tangent will be positive. However, if sine is positive while cosine is negative (or vice versa) the tangent graph will be negative which in the end makes the pattern of +-+-.
Cotangent
The picture above shows a picture that contains sine, cosine, and now cotangent. Cotangent is basically the same thing as tangent in ways that it contains sine and cosine in its trig ratio. However, cosine is now the numerator and sine is the denominator. Again we must follow the ideas of where each trig function is positive or negative depending on the unit circle so we can know what direction to draw it. Apart from this, the asymptotes for a cotangent graph is different than a tangent graph.
Secant
The trig function secant , as we know, is the reciprocal of cosine. This makes its trig ratio be 1/cosine. Since we know that it coexists with cosine, we are able to notice the asymptotes so that we can be able to graph the points and make a graph that looks like the blue line above.
Cosecant
For a cosecant graph, we know that the reciprocal for this trig function is sine. Since we know that cosecant coexists with sine, we are able to plot the asymptotes (such as secant) and be able to plot the graph which will always look like the black line.
References
https://www.desmos.com/calculator/hjts26gwst
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