Derivatives of Trigonometric Functions

anpanman SG

Find the equations of the tangent and the normal to the curve y = 1 + cos x at the point where x = pi/6. Show that the area enclosed by the tangent, normal and the x-axis is 5/4 (1 + sq.3 /2)^2

No problem getting the equations. However, I do not understand the workings and concept behind this area thing. How can I make use the the equations I have to derive the area?

Thank you.

SBS n SMRT SG

this must be Qn 8 from Panpac A Maths

U had eqns of normal ,tangent and x-axis

the three axis form a triangle

the normal and tangent intercept at a point, that is the upper vertice of the triangle

the normal and tangent intercept x-axis is the coordinates of the base length of the triangle

find length of height and base

den using triangle formulae, find area

anpanman SG

Thanks SBS n SMRT (:

The volume of water in a container V (cm3) after t seconds is given by V = 20e^-1/5. Find, in terms of e, the rate of change of V when t = 5.

Answer is -4/e but I got 4/e. Would need the full solution for this question if possible... Anyway, this question doesn't require me to rearrange a formula of my own, does it? (eg. dy/dt = dy/dx X dx/dt)

wee_ws SG

Hi,

-4/e is correct. Do check your working. There is no need to use chain rule. Thanks!

Cheers,
Wen Shih

anpanman SG

Hi. I still can't get the answers for both questions somehow.... is it possible to show me the workings? thanks. i really need help for the first question.

*Edited: Managed to find the answer to question 2. (: I only need help in solving question 1.

wee_ws SG

Hi,

Draw the triangle so that you can see what the height and base of the triangle are.

Thanks!

Cheers,
Wen Shih

SBS n SMRT SG

Thanks SBS n SMRT (:

The volume of water in a container V (cm3) after t seconds is given by V = 20e^-1/5. Find, in terms of e, the rate of change of V when t = 5.

welcme.....