solve [1-cos(7pi/4)]/2
To solve the expression (1 - cos(7π/4))/2, we need to follow these steps:
Step 1: Evaluate cos(7π/4).
We can find the value of cos(7π/4) by knowing the values of cos for standard angles.
The angle 7π/4 is equivalent to 315 degrees, which lies in the fourth quadrant on the unit circle.
In the fourth quadrant, the cosine function is negative, so cos(7π/4) = -√2/2.
Step 2: Substitute the value into the expression.
Substituting the value of cos(7π/4) into the expression (1 - cos(7π/4))/2, we get:
(1 - (-√2/2))/2
Simplifying this expression gives us:
(1 + √2/2)/2
Step 3: Rationalize the denominator.
To rationalize the denominator, multiply both the numerator and denominator by the conjugate of the denominator.
The conjugate of 2 is 2, so we multiply numerator and denominator by 2:
(1 + √2/2)(2)/2(2)
Simplifying further, we have:
2 + √2/4
Therefore, the solution to the expression (1 - cos(7π/4))/2 is 2 + √2/4.