 In this video, we present the solution to question number 10 for practice exam number two for math 1060. We're asked to sketch one complete cycle of the graph y equals tangent of 2x. And we need to make sure we include any vertical asymptotes on the graph because tangent does in fact have vertical asymptotes. So we look at this graph y equals tangent of 2x. What does this two do to things? Well, the standard period of a tangent or a cotangent curve is pi. And so that coefficient of two is gonna cut that in half. So the period is gonna be pi halves. So thinking of the standard tangent, which normally your vertical asymptotes would be from negative pi halves to pi halves, we're gonna cut this in half. There's a horizontal compression by factor of two. So we're gonna have vertical asymptotes now at pi force and negative pi force because we've cut this in half. And then everything else is the same. So I'm just gonna draw my standard tangential graph right here between my vertical asymptotes. I only need one period. So I can graph them from negative pi force to pi force. That'll give you the complete picture. If you wanna graph more than that, that's okay. But only one complete cycle is required. And so I'm just gonna graph the principal branch of this tangent curve from negative pi force to pi force.