Study guides

Q: How was it determined that the tangent of pi divided by 4 is 1?

Write your answer...

Submit

Still have questions?

Related questions

tangent of pi/4 = 1

If you have an angle of (pi/4+k*pi) or pi*(0.25+k) radians where k is an integer.

0.5

1

9

It is a function which maps the tangent ratio - any real value - to an angle in the range (-pi/2, pi/2) radians. Or (-90, 90) degrees.If tan(x) = y then x is the inverse tangent of y.It is also known as "arc tangent", and spreadsheets, such as Excel, use "atan" for this function.Warning:1/tangent = cotangent is the reciprocal, NOT the inverse.

sin (pi/2) = 1

It is 2*pi/3.

1/2

Because it tends to infinity. Additionally, tangent can be expressed as sin theta divided by cos theta. The sine of 90 is 1. The cosine of 90 is 0. That would be 1 divided by 0, or division by zero; which is undefined.

In 1761, Joseph Lambert proved that pi was irrational by basically proving that the tangent of some number x could be expressed as a particular continued fraction as a function of x. He then went on to show that if x was rational, the continued fraction must be irrational, and since the tangent of pi/4 was 1 (i.e. rational), then pi/4 and thus pi itself must not be rational.

28

People also asked