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Solving cos 3x = -0.24

I need to work out the coordianates of the equation cos 3x = -0.24 in the ranges of 0 <= x <= 360. I have correctly worked out some of the cordinates but some of the intervals are missing. What I have so far:

360 * 3 = 1080, so the range is 0 <= x <= 1080

cos-1 (-0.24) = 103.886

First: 103.886 / 3 = 34.6
Second: 360 - 103.9 = 256.1, 256.1/3 = 85.4
Third: 360 + 103.9 = 463.9, 463.9 / 3 = 154.6
Fourth: 463.9 + 360 = 823.9, 823.9 / 3 =274.4

These are correct, but I am missing the values 205.4 and 325.4, where have I gone wrong?
Reply 1
Avatar for RichE
RichE
15
Original post by Simon33355
I need to work out the coordianates of the equation cos 3x = -0.24 in the ranges of 0 <= x <= 360. I have correctly worked out some of the cordinates but some of the intervals are missing. What I have so far:

360 * 3 = 1080, so the range is 0 <= x <= 1080

cos-1 (-0.24) = 103.886

First: 103.886 / 3 = 34.6
Second: 360 - 103.9 = 256.1, 256.1/3 = 85.4
Third: 360 + 103.9 = 463.9, 463.9 / 3 = 154.6
Fourth: 463.9 + 360 = 823.9, 823.9 / 3 =274.4

These are correct, but I am missing the values 205.4 and 325.4, where have I gone wrong?

What about 720-103.9? Was that on your list?
Original post by Simon33355
I need to work out the coordianates of the equation cos 3x = -0.24 in the ranges of 0 <= x <= 360. I have correctly worked out some of the cordinates but some of the intervals are missing. What I have so far:

360 * 3 = 1080, so the range is 0 <= x <= 1080

cos-1 (-0.24) = 103.886

First: 103.886 / 3 = 34.6
Second: 360 - 103.9 = 256.1, 256.1/3 = 85.4
Third: 360 + 103.9 = 463.9, 463.9 / 3 = 154.6
Fourth: 463.9 + 360 = 823.9, 823.9 / 3 =274.4

These are correct, but I am missing the values 205.4 and 325.4, where have I gone wrong?


Fourth is actually just: 360*2 + 103.9 = 823.9

Fifth is 360*2 - 103.9

Sixth is 360*3 - 103.9

Seventh would be 360*3 + 103.9 but thats outside the range 0 <= 3x <= 1080. No need to go further.
Original post by Simon33355
I need to work out the coordianates of the equation cos 3x = -0.24 in the ranges of 0 <= x <= 360. I have correctly worked out some of the cordinates but some of the intervals are missing. What I have so far:

360 * 3 = 1080, so the range is 0 <= x <= 1080

cos-1 (-0.24) = 103.886

First: 103.886 / 3 = 34.6
Second: 360 - 103.9 = 256.1, 256.1/3 = 85.4
Third: 360 + 103.9 = 463.9, 463.9 / 3 = 154.6
Fourth: 463.9 + 360 = 823.9, 823.9 / 3 =274.4

These are correct, but I am missing the values 205.4 and 325.4, where have I gone wrong?


can i just ask, do you use a graph sketch or do you use the CAST diagram for these calculations
Reply 4
Avatar for Simon33355
Simon33355
OP
9
Original post by RichE
What about 720-103.9? Was that on your list?


No everything I worked out, I have shown. How do I know when to subtract from 360?

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