# What is the equation of the tangent to the curve  y=9tanx  at the point where x=(2pi)/3?

What is the equation of the tangent to the curve  y=9tanx  at the point where x=(2pi)/3?

ReportAnswer 1

$y = 36 x - 24 \pi - 9 \sqrt{3}$

#### Explanation:

$y = 9 \tan x$

Differentiating wrt $x$ gives:
$\frac{\mathrm{dy}}{\mathrm{dx}} = 9 {\sec}^{2} x$

So, When $x = \frac{2 \pi}{3} \implies y = 9 \tan \left(\frac{2 \pi}{3}\right) = - 9 \sqrt{3}$
and, $\frac{\mathrm{dy}}{\mathrm{dx}} = 9 {\sec}^{2} \left(\frac{2 \pi}{3}\right) = 9 {\left(- 2\right)}^{2} = 36$

Thus, the tangent has gradient $m = 36$ and passes through $\left(\frac{2 \pi}{3} , - 9 \sqrt{3}\right)$

So, using $y - {y}_{1} = m \left(x - {x}_{1}\right)$ the required equation is:
 y-(-9sqrt(3))) = 36(x-(2pi)/3) 
$\therefore y + 9 \sqrt{3} = 36 x - \frac{72 \pi}{3}$
$\therefore y = 36 x - 24 \pi - 9 \sqrt{3}$

answered by: Steve M Shwetank Mauria
##### Add Answer of: What is the equation of the tangent to the curve  y=9tanx  at the point where x=(2pi)/3?
Similar Homework Help Questions

• ### Find the slope of the tangent to the curve y=2/(x+3) at the point where x=a

Find the slope of the tangent to the curve y=2/(x+3) at the point where x=a.

• ### Find the equation of the tangent to the curve defined by y = lnx2 / x at the point where x = 4.

Find the equation of the tangent to the curve defined by y =lnx2 / x at the point where x = 4.The answer is: (1 - ln4)x - 8y + (8ln4 - 4) = 0

• ### find the coordinates of the point where the tangent to the curve y=x^3 +x +2 at the point (1,4) meets the curve again

find the coordinates of the point where the tangent to the curve y=x^3 +x +2 at the point (1,4) meets the curve again. [ans:-2,-8]pls help me i dont understand the question....

• ### Find the equation of the tangent to the curve define by y=lnx^2/x at the point where x=4?

y = (ln x2 ) / x

• ### What is the slope of the tangent line to the curve y=x-x^3 at the point (1,0)? Please use the definition of a derivative function and not the power function. As you go along, also please explain the algebraic methods used to simplify youranswer (rather just writing what you've gotten after using algebra). I need to brush up on algebra and so this is very helpful to me.I cannot simplify further after Thank you.

• ### find the slope of the tangent to the curve y = 3+4x^2-2x^3 at the point where x=a

find the slope of the tangent to the curve y = 3+4x^2-2x^3 at the point where x=a

• ### Find the slope of the tangent to the curve at the point where x = a.

lim 4+(4x^2)-(2x^3)x-a

Need Online Homework Help?