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Higher Maths

Could anyone help me with this question?

Solve algebraically the equation 5sin2x = 10cosx for 0 < or equal to x < 360
Original post by Sthat
Could anyone help me with this question?

Solve algebraically the equation 5sin2x = 10cosx for 0 < or equal to x < 360


You need to use:

sin(2x)=2sin(x)cos(x)sin(2x) = 2sin(x)cos(x)
Reply 2
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Notnek
21
Original post by Sthat
Could anyone help me with this question?

Solve algebraically the equation 5sin2x = 10cosx for 0 < or equal to x < 360

As soon as you see sin⁡2x\sin 2x, you should think about using an identity.

Have you tried this? Please post any working that you've done.
Reply 3
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Sthat
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Original post by notnek
As soon as you see sin⁡2x\sin 2x, you should think about using an identity.

Have you tried this? Please post any working that you've done.


I have not, I don't really know how to start answering it.
Reply 4
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Notnek
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Original post by Sthat
I have not, I don't really know how to start answering it.

SherlockHolmes gave you the identity that you should be using. Have you seen this identity before?

So start by replacing sin⁡2x\sin 2x with 2sin⁡xcos⁡x2\sin x \cos x.
Reply 5
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Sthat
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Original post by notnek
SherlockHolmes gave you the identity that you should be using. Have you seen this identity before?

So start by replacing sin⁡2x\sin 2x with 2sin⁡xcos⁡x2\sin x \cos x.


Okay so after doing that it becomes 10sinxcosx = 10cos x
I then rearranged it to 10sinxcosx - 10cosx = 0 and then cosx(10sinx-10) = 0

Is that right?
Reply 6
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Notnek
21
Original post by Sthat
Okay so after doing that it becomes 10sinxcosx = 10cos x
I then rearranged it to 10sinxcosx - 10cosx = 0 and then cosx(10sinx-10) = 0

Is that right?

Yes that's correct. Can you carry on from there?
Reply 7
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Sthat
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Original post by notnek
Yes that's correct. Can you carry on from there?


There's more? haha woops I thought that was the end.
This is A Level maths, right?
Original post by Carthaginian
This is A Level maths, right?


Nope, the Scottish Equivalent.

The proper definition would be SQA Higher CFE Maths.
Original post by MathsAndCoffee
Nope, the Scottish Equivalent.

The proper definition would be SQA Higher CFE Maths.


Ah, thought this was GCSE level and got scared asf.
Reply 11
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Notnek
21
Original post by Sthat
There's more? haha woops I thought that was the end.

You need to solve it to find values of x that satisfy the equation.

Now you've factorised the next step is to solve it like you would a quadratic with two brackets:

( ... )( ... ) = 0
Original post by Carthaginian
Ah, thought this was GCSE level and got scared asf.


Our GCSE is national 5 / intermediate 2.

Higher is A1

Advanced Higher is A2

Correct me if I'm wrong.
Reply 13
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Sthat
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5
Original post by notnek
You need to solve it to find values of x that satisfy the equation.

Now you've factorised the next step is to solve it like you would a quadratic with two brackets:

( ... )( ... ) = 0


Would you be able to help me with this question?

IMG_0495.jpg
Original post by Sthat
Would you be able to help me with this question?

IMG_0495.jpg


you need to integrate 4cos(2x) with respect to x, using limits 0 and π/4
Original post by Sthat
Would you be able to help me with this question?

IMG_0495.jpg


Integral of 4cos2xdx = 2sin2x.
Substitute in the limits between pi/4, 0.
(2sin2(pi/4) - (2sin2(0)
(2sin(90)) - 0
sin90= 1

2x1= 2units squared!

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