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# Consider the following points on the graphs of and, with the added vertical dashed lines:

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Consider the following points on the graphs of $$y = cos(x)$$ and,$$y = \cos(x + \pi/6)$$ with the added vertical dashed lines:

Then what are 10c and 10d in that order?

Apr 2, 2022

#1
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10c = 5*sqrt(3) - 1, 100d = 5*sqrt(3) + 2

Apr 2, 2022
#2
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Hello sir, the answer is wrong

Guest Apr 2, 2022
#3
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I will do the more difficult one and then you can almost copy and do the easier one.

'a' is a negative number so to stop my own confusion I let   a=-t    (so t is positive)

Now

cos(t)=0.8

$$c=cos(-t+\frac{\pi}{6}) \\ c=cos(\frac{\pi}{6}-t )\\ c=cos(\frac{\pi}{6})cos(t)+sin(\frac{\pi}{6})sin(t)\\ c=\frac{\sqrt3}{2}*0.8+\frac{1}{2}*0.6\\ 10c=\frac{\sqrt3}{2}*8+\frac{1}{2}*6\\ 10c=4\sqrt3+3$$

If you do not understand then ask specific question, the mothod is almost identical.

LaTex:

c=cos(-t+\frac{\pi}{6}) \\
c=cos(\frac{\pi}{6}-t )\\
c=cos(\frac{\pi}{6})cos(t)+sin(\frac{\pi}{6})sin(t)\\
c=\frac{\sqrt3}{2}*0.8+\frac{1}{2}*0.6\\
10c=\frac{\sqrt3}{2}*8+\frac{1}{2}*6\\
10c=4\sqrt3+3

Apr 3, 2022