Andrew M. answered • 04/02/16
Tutor
New to Wyzant
Mathematics - Algebra a Specialty / F.I.T. Grad - B.S. w/Honors
4(cos4x) = 0
Divide both sides by 4 to get cos4x
alone on the left side of the equation
4(cos4x)/4 = 0/4
cos4x = 0
At this point, if you knew that cos90 = 0 you could
immediately set 4x=90 and solve for x, otherwise:
We need to use the inverse cosine function to
solve this
Note: cos-1 means "inverse cosine"
cos-1[cos4x] = cos-10
4x = cos-10
4x = 90
Divide both sides by 4 to get a single x
90/4 = 4x/4
22.5 = x
x = 22.5
You can verify the answer by plugging 22.5 in place
of x in the original equaton.
4(cos(4*22.5)) = 0
4cos90 = 0
4(0) = 0
0 = 0
The equation balances and fits the information given
Andrew M.
Picture a circle with center at the origin (0,0).
and raduis 1. ... For each degree around the
circle, the cosine value equates to the x coordinate
and the sine equates to the y coordinate.
90 degrees equates to the point
(0,1) and the cosine is the x coordinate.
Cos90 = 0
sin90 =1
cos0 = 1
sin0 = 0
equating to the point (1,0)
What you have here is essentially
cos4x = 0
so 4x=90 because cos90 = 0
thus x=90/4 = 22.5
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04/03/16
Pia R.
Thanks but how abt cos270?
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04/03/16
Andrew M.
Picture the circle....
270 degrees would correspond to the point (0,-1)
Cosine 270 = 0
Sine 270 = -1
So..., Actually, you are correct. My apologies.
4x = 90, x = 22.5
4x = 270, x = 67.5
Two answers
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04/03/16
Andrew M.
The calculator gave inverse cosine of zero as 90
and I didn't look past that. Very nice catch.
Obviously, you got the idea of the relationship
between the cosine, sine and the circle. Fantastic.
:-)
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04/03/16
John G.
If you need to find all values of x between 0 and 360 (or 0 to 2pi), there would be 8 answers. If x goes from 0 to 360, then 4x goes from 0 to 1440.
For example, 90, 450, 810, and 1170 are all coterminal (just adding 360 each time), but if we set them equal to 4x, then you get 4 angles that make your equation work. The same goes for 270 and its coterminal angles up to 1350.
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04/03/16
Pia R.
thank you so much john and andrew! you guys rock!
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04/12/16
Pia R.
04/02/16