Question

The slope of the tangent to the curve $y=\sin 2x+2\sin x$ at $x=\frac{\pi }{3}$ is given by?

• A. $0$
• B. $\frac{\pi }{3}$
• C. $1$
• D. $-1$

Answer 1

The correct option is A $0$

curve y = sin 2x+2 sinx

slope of curve means derivative of the curve

$\frac{dy}{dx}$ = 2 cos2x+2cosx

$\left[\right(sin2x)=cos2x(2x)=2cos2x]$

$\frac{dy}{dt}atx=\pi /3$ is

$2cos\left(\frac{2\pi }{3}\right)+2cos\pi /3$

$2cos(\frac{\pi }{2}+\frac{\pi }{6})+2cos\pi /3$

$\left[cos\right(\frac{\pi }{2}+x)=-sinx][cos\pi /3=1/2]$

$-2sin\pi /6+2\left(1/2\right)[sin\pi /6=\frac{1}{2}]$

$-2\left(\frac{1}{2}\right)+1=-1+1=0$