SOLUTION: Please help me solve {{{sqrt ( 4 )cos (x-0.588) = 1 }}}

Question 826270: Please help me solve

Answer by jsmallt9(3758) (Show Source): You can put this solution on YOUR website!

First, we need to transform the equation into the general form:
function(expression) = number

We'll start with simplifying. Since :

Dividing both sides by 2:

And we have the desired form.

The next step is to determine the reference angle and the quadrants. We should recognize that 1/2 is a special angle value for cos. We should know that a reference angle of has a cos of 1/2. Also, the 1/2 is positive and cos is positive in the 1st and 4th quadrants. From this we should get the following general solution equations:
for the 1st quadrant
for the 4th quadrant
Adding 0.588 to each side of both equations we get:

Using various integer values for "n" in these equation will give us values for x which fit the original equation.

Often these problems ask for solutions in a specific interval. For this we would actually try various n's looking for all the solutions within that interval. This problem, as you posted it, does not do this. So the general solution equations (i.e. all solutions):

are the answer to the problem.
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