Question

Write the equation of a tangent to the graphs of the following curves at the indicated points
$y=\sin x+1$ at the point $x$ = $\pi /2.$

Answer 1

To find : - equation of tangent of $y=\sin x+1$ at $x=\frac{\pi }{2}$

First, put $x=\frac{\pi }{2}$ in $y$

$y_0=\sin \frac{\pi }{2}+1=1+1=2$

Now, $y^{\prime }=\cos x+0=\cos x$

Now, put $x=\frac{\pi }{2}$ in $y^{\prime }$

$y^{\prime }=\cos \frac{\pi }{2}=0$

Use point - slope equation : -

$(y-y_0)=m(x-x_0)$ where

$y_0=2,m=0,x_0=\frac{\pi }{2}$

$(y-2)=0(x-\frac{\pi }{2})$

$y=2$.