# Maths C3 Help

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#1
The function y=sin^3x has five stationary points in, negative pi is less than or equal to x and positive pi is greater than or equal to x.
Find dy/dx and find the coordinates of the five stationary points:
I have found dy/dx: 3cosxsin^2x and made it equal to zero but don't know where to go from there!! Any help would be greatly appreciated.
0
4 years ago
#2
The equation 3cosxsin^2x=0 has solution between -pi and pi where either cos x is zero or sin^2x is zero.

sin^2 x is zero at -pi, 0 and pi. Cos x is zero at -pi/2 and +pi/2 and so you have turning points at -pi, -pi/2, 0, pi/2 and pi.

To see them, plot sin^3x and 3cosxsin^2x on the same axes. (fooplot.com is good). (attached)

0
4 years ago
#3
(Original post by metaljoe)
The function y=sin^3x has five stationary points in, negative pi is less than or equal to x and positive pi is greater than or equal to x.
Find dy/dx and find the coordinates of the five stationary points:
I have found dy/dx: 3cosxsin^2x and made it equal to zero but don't know where to go from there!! Any help would be greatly appreciated.
When solving trigonometric equations in C2 you used identities to simplify equations that had a mixture of trig functions.
Use one of those identities to replace the sin^2x and rewrite in terms of just cosx
Factorise.

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#4
(Original post by nerak99)
The equation 3cosxsin^2x=0 has solution between -pi and pi where either cos x is zero or sin^2x is zero.

sin^2 x is zero at -pi, 0 and pi. Cos x is zero at -pi/2 and +pi/2 and so you have turning points at -pi, -pi/2, 0, pi/2 and pi.

To see them, plot sin^3x and 3cosxsin^2x on the same axes. (fooplot.com is good). (attached)

Thank you for the help!! Have a nice rest of your week
0
#5
(Original post by gdunne42)
When solving trigonometric equations in C2 you used identities to simplify equations that had a mixture of trig functions.
Use one of those identities to replace the sin^2x and rewrite in terms of just cosx
Factorise.

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I will use the advice. Thank you !!
0
4 years ago
#6
(Original post by metaljoe)
I will use the advice. Thank you !!
It is worth pointing out that 3cosxsin^2x=0 is already factorised and going through the process described by gdunne42 is possible but entirely redundant.
0
4 years ago
#7
(Original post by nerak99)
It is worth pointing out that 3cosxsin^2x=0 is already factorised and going through the process described by gdunne42 is possible but entirely redundant.
True, I didn't consider that when I looked at it. Guess I was locked in trig identity mode from doing other questions.

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