Question

How do you evaluate tan(3π/4)?

Answer 1

First, convert to degree form. This is much easier to input into your calculator, and it is important to learn how to convert the two forms.

Explanation:

Convert to degree form by multiplying by the ratio `180/pi`

`tan((3pi)/4)(180/pi)`

The `pi`'s eliminate themselves, and the 180 becomes divided by the 4. This give us 45. The 3 stays:

tan(`3 xx 45`)

= tan`75`

Now you can evaluate it with a calculator. Make sure that the calculator is in degree setting, noted on most calculators by "deg".

Practice exercises:

1. Evaluate:

a). `cos132` degrees

b). `sin((5pi)/2)`

Answer 2

`tan(3pi)/4 = -1`

Explanation:

`tan((3pi)/4)` by definition is `(sin((3pi)/4)) / (cos((3pi)/4))`
`sin((3pi)/4)` by definition is an ordinate of a point on a unit circle with an angle from the positive direction of the `x`-axis to a radius to this point equaled to `(3pi)/4`.
`cos((3pi)/4)` by definition is an abscissa of this same point.
This point lies on an angle bisector of the second quadrant and, therefore, has coordinates `{-sqrt(2)/2; sqrt(2)/2}`, where X-coordinate representing `cos((3pi)/4)` and Y-coordinate representing `sin((3pi)/4)`.
Therefore, `(sin((3pi)/4)) / (cos((3pi)/4)) = (sqrt(2)/2) / (-sqrt(2)/2) = -1`

I hope that helps!