Find an equation of the line tangent to the curve y = sin x at...

Question

Find an equation of the line tangent to the curve y = sin x at x = 0.

Accepted Answer

Welcome back, everyone. Find an equation of the line tangent to the curve Y equals cosine of X at X equals pi divided by 2. We're given 4 answer choices A plus y equals x minus pi divided by 2, B X plus pi divided by 2, C X plus pi, and D X minus pi. So what we want to do is simply define the equation of a tangent line. The equation of the tangent line is y equals. F prime the derivative of the given function at the point of interest x not multiplied by x minus x plus F at x0, which is the value of the function at that point and we given the point of interest it's X0 equals pi divided by 2. The function of interest is F of X equals cosine of x. So what we want to do is evaluate the slope at the given point. And for that purpose we want to differentiate. F of X, which is the derivative of cosine of x based on the table of basic derivatives, this is a negative sine of x, right? And now let's evaluate the slope at the given point. So F at point pi divided by 2 is negative sign of pi divided by 2. So we get negative and sine of pi divided by 2 is equal to 1. So our slope is -1, and we also want to identify the value of the function at that point. So F at pi divided by 2 is the value of the function at pi divided by 2, and our function is cosine x, so we substitute X equals pi divided by 2. And cosine of pi divided by 2 is 0. So our equation becomes y equals -1 or simply negative in paris x minus x0 so x minus pi divided by 2 plus F at point X0. So F at point divided by 2, which is 0. And now let's distribute the terms. We get negative X minus minus gives us plus pi divided by 2. And we have obtained the equation of the tangent line to the curve Y equals cosine of X at x equals pi divided by 2. This equation corresponds to the answer choice b. Thank you for watching.

Find an equation of the line tangent to the curve y = sin x at x = 0.

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