SOLUTION: How many solutions of the trigonometric equation cos 𝑥 = 0.7 are in the interval [−𝜋; 2𝜋]

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Question 1199541: How many solutions of the trigonometric equation cos 𝑥 = 0.7 are in the interval [−𝜋; 2𝜋]
Found 2 solutions by ikleyn, greenestamps:
Answer by ikleyn(52803) About Me  (Show Source):
You can put this solution on YOUR website!
.

The solutions to the given equation in the given interval are close to

        -pi%2F4,   pi%2F4,   7pi%2F4.

In all,  there are  3  (three)  such solutions.         ANSWER



Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


cos(x) takes on all its values (between -1 and 1) on the interval from 0 to pi. It similarly takes on all its values on any interval from (n)pi to (n+1)pi.

The given interval consists exactly of three of those intervals, so the equation is satisfied 3 times on the given interval.