Calculus 8th Edition

Published by Cengage
ISBN 10: 1285740629
ISBN 13: 978-1-28574-062-1

Chapter 2 - Derivatives - 2.4 Derivatives of Trigonometric Functions - 2.4 Exercises: 21

Answer

The tangent line formula is: $y=x+1$

Work Step by Step

First derivate the function $y'=\cos(x)-\sin(x)$ Then substitute the given point in the derivate. The derivate represents the slope of the curve in any point $y'(0,1)=\cos(0)-\sin(0)=1$ So we have that $m=y'=1$ Remember the rect line formula $y=mx+b$ Let's find b (the displacement) $b=y-mx=(1)-(1)(0)=1$ So the tangent line formula is: $y=x+1$
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