Solve for x cos(x)=-( square root of 2)/2

Problem

cos(x)=−√(,2)/2

Solution

1. Identify the reference angle by finding the value of θ such that cos(θ)=√(,2)/2 in the first quadrant.

θ=π/4

2. Determine the quadrants where the cosine function is negative.

Quadrants II and III

3. Calculate the specific solutions within the interval [0,2*π) by applying the reference angle to the identified quadrants.

x=π−π/4=(3*π)/4

x=π+π/4=(5*π)/4

4. Generalize the solution to include all possible angles by adding integer multiples of the period 2*π where n is any integer.

x=(3*π)/4+2*n*π

x=(5*π)/4+2*n*π

Final Answer

cos(x)=−√(,2)/2⇒x=(3*π)/4+2*n*π,(5*π)/4+2*n*π

Want more problems? Check here!