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If the trigonometric equation involves a tangent function rather than sine or cosine, what would change?

that's such a general question it's hard to answer. I guess you could always use the fact that

tanx = sinx/cosx

to reduce it to a bunch of sine/cosine stuff

Did you know?

Did you know that if a trigonometric equation involves a tangent function instead of sine or cosine, there are some key differences? Unlike sine and cosine functions, the tangent function does not have a period of 2π. Instead, its period is π, meaning it repeats every π radians or 180 degrees. This is because the tangent function is equivalent to the ratio of sine over cosine, so it takes on the same value at every π radians. Furthermore, the tangent function has vertical asymptotes at intervals of π radians apart. These asymptotes represent values where the tangent function approaches positive or negative infinity, and they occur whenever the cosine function is equal to zero. So, the next time you encounter a trigonometric equation involving a tangent function, remember that its period is π and it has vertical asymptotes at regular intervals. These unique properties make the tangent function distinctive compared to sine and cosine.