What is the exact circular function value for tan pi/4
To determine the exact circular function value for tan(pi/4), we can use the unit circle.
Step 1: Draw a circle with a radius of 1 unit.
Step 2: Divide the circle into four quadrants.
Step 3: Mark the point on the circle corresponding to the angle pi/4. This angle is equal to 45 degrees.
Step 4: Draw a line from the center of the circle to the marked point.
Step 5: The coordinate where the line intersects the circle gives us the values of sine, cosine, and tangent.
Since the angle pi/4 corresponds to 45 degrees, it lies in the first quadrant of the unit circle. In this quadrant, the x-coordinate is equal to the cosine value, and the y-coordinate is equal to the sine value.
For pi/4 or 45 degrees, the coordinates are (cos(pi/4), sin(pi/4)).
Now, let's determine the values of sine, cosine, and tangent for pi/4:
cos(pi/4) = sqrt(2)/2
sin(pi/4) = sqrt(2)/2
tan(pi/4) = sin(pi/4) / cos(pi/4) = (sqrt(2)/2) / (sqrt(2)/2) = 1
Therefore, the exact circular function value for tan(pi/4) is 1.