Find the equation of the tangents to the curve Y equal cosine X at X equal negative π halves Pi halves into π. Then graph the curve over the interval together with the tangents. Label each curve in tangent. So if we're trying to find the tangents, we're going to need the slope. So the derivative of cosine X is negative sine X. Finding Y prime at negative π halves, Pi halves and 2π. So Y prime and negative π halves is negative sign of negative π halves. Knowing our unit circle, sine and negative π halves is -1 and the opposite of -1 is one. Y prime of π halves is negative sine Pi halves. Well, sine of π halves is one, so the opposite of 1 or -1 Y prime of 2π negative sine 2π sine of 2π is 0. We also need our Y values if we're going to find our tangent, because we're going to use point slope. So Y of negative π halves cosine of negative π halves IS0Y of π halves cosine Pi halves is 0 and Y of 2π cosine of 2π is 1. So now we have points negative π halves, zero with a slope of one Pi halves, zero with a slope of -1 and 2π, one with a slope of 0. Putting it in a point slope form and solving for Y, we get Y equal X + π halves, Y equal negative, X + π halves and Y equal 1. It wants us to graph it. So we need to graph a cosine curve and then when we look at negative π halves we need a positive slope of one. When we look at Pi halves, we need a slope of -1 and at 2π we need a slope of 0.