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Solve for 0 ≤ Θ ≤ 2π
cos Θ = 1/4

I got one answer which is ~1.32 by taking the inverse cos of 1/4 and converting to radians, but my book gives me another answer which is ~4.97.

Also, is my method correct?
thanks

2007-12-05 22:14:29 · 4 answers · asked by fye 1 in Science & Mathematics Mathematics

4 answers

sin | All
---------
tan| cos

Above diagram indicates that cos θ is + ve in 1st AND 4th quadrants.

cos θ = 1/4
θ = 1.32 , 2π - 1.32
θ = 1.32 , 4.96

2007-12-05 23:54:31 · answer #1 · answered by Como 7 · 2 1

Correct. Your first answer is in the first quadrant. think of cos as x, i.e. left or right of the y axis.
A a plus value of 0.25, cos theta is to the right of the y axis.
the other answer is in the fourth quadrant at 2pi - 1.32 = 4.97

Here is your 'homework'. Learn ASTP for the four quadrants, and use a unit circle. Practise with 1) cos(theta) = sq_rt(3)/2 and 0<= theta <= 360 degrees. Write down the two answers in degrees. 2) sin(theta) = - 0.5 write down the two answers in degrees, given that 0<=theta <= 360 degrees.

2007-12-05 22:31:45 · answer #2 · answered by Sciman 6 · 0 1

your method is correct,but you have to remember that there are two angles in this domain that have their cos = + 1/4
one of them is in the first quadrant, which is your answer = 1.32. and the other is in the fourth quadrant which is (2pi - 1.23) try this on your calculator and you will find it 4.97

2007-12-05 22:30:53 · answer #3 · answered by Anonymous · 2 1

cos x = 1/4 has two solutions on that interval
because cos(x)=cos(-x)
So if you have a solution, its negative is a solution too.
Your method is good though I think the answer is already in radians, so you don't need to convert.
I guess.

2007-12-05 22:25:27 · answer #4 · answered by Theta40 7 · 1 2

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