Solve for x cos(x)=-4/5

Problem

cos(x)=−4/5

Solution

1. Identify the range of the inverse cosine function. To find the principal value, we use x=arccos(−4/5) which yields an angle in the second quadrant because the cosine value is negative.

2. Calculate the principal value. Using a calculator for the inverse cosine of −0.8

x≈2.498* radians

x≈143.13

3. Determine the general solution. Since cosine is a periodic function with a period of 2*π and cos(x)=cos(−x) the solutions are found by taking the positive and negative of the principal value and adding multiples of 2*π

x=±arccos(−4/5)+2*π*n

4. Express the solution using an integer constant n where n is any integer (n∈ℤ.

Final Answer

cos(x)=−4/5⇒x=±arccos(−4/5)+2*π*n

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