You are watching: How to get answers in terms of pi on ti 84

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*.

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.

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.

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