Trigonometric functions as fractions on TI-84 Plus.

Question

I know that on the TI-84, you can use mode to change settings to fraction mode. However, when I used trigonometric functions to convert them into fractions, they gave me decimals still. Is there another step you have to take in order to receive fractional answers for trigonometric functions? E.g. In radians, cos(pi/3), which equals (sqrt(3))/2, but the calculator gives .866025...

Answer 1

As the other answer says, you simply can't express all values of trigonometric functions as fractions.

I am guessing that on your TI-84, if you set the calculator to give you the fractions, then $\sin(30^\circ) = \sin(\pi /6)$ will give you $\frac{1}{2}$ (that is how it works on my TI-84). But you also know that, for example, $\sin(45^\circ) = \sin(\pi / 4)$ is equal to $\frac{\sqrt{2}}{2}$. This is not a rational number and can't be written as a ratio of two integers.

You calculator can only find these exact fractions when the answer is a rational number.

Answer 2

The trigonometric functions are examples of transcendental functions, which implies that most of their values are irrational numbers, i.e. cannot be expressed as fractions of integers (more formally called a rational number). However, you can always convert a decimal number to an approximate fraction. For example, $$\pi=3.1415926535897932384... \approx 3.14159 = \frac{314159}{1000000}$$ and you can simplify that last fraction if you want.

Answer 3

Old question, but I have something to add. If you are working arcsin for example, the answer will be some fraction multiplied by pi, such will not get represented by the calculator (something I don't understand as my $10 walmart calculator does it with no problem); however, you can counter this by dividing out the pi and converting that result to a fraction, then multiply the pi back into its numerator.