Simplify arccos(1/( square root of 2))

Problem

arccos(1/√(,2))

Solution

1. Identify the value inside the inverse trigonometric function. We are looking for an angle θ such that cos(θ)=1/√(,2) within the restricted range of the arccosine function, which is [0,π]

2. Rationalize the denominator of the input to recognize it from the unit circle.

1/√(,2)⋅√(,2)/√(,2)=√(,2)/2

3. Determine the angle in the first quadrant where the cosine value is √(,2)/2 From the standard values of trigonometric functions, we know that cos(π/4)=√(,2)/2

4. Conclude that since π/4 is within the interval [0,π] it is the principal value.

Final Answer

arccos(1/√(,2))=π/4

Want more problems? Check here!