Find the indicated function value. Do not use a calculator.
tan 180 degrees
think of a rotating arm of length 1 rotating about the origin (0,0)
at 180º the end of the arm will land on (-1,0)
tan (theta) = y/x
tan 180 = 0/-1 = 0
To find the value of the tangent of 180 degrees without a calculator, we can use the reference angle and the properties of the tangent function.
The tangent function is defined as the ratio of the sine of an angle to the cosine of the same angle. Since we are looking for the tangent of 180 degrees, we can use the reference angle of 180 degrees, which is 0 degrees.
The value of the tangent function at 0 degrees is zero, since the sine of 0 degrees is also zero and the cosine of 0 degrees is 1. Thus, tan 180 degrees is 0.