# Trigonometric functions as fractions on TI-84 Plus.

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...

• which functions do you mean? – Dr. Sonnhard Graubner Jul 17 '15 at 12:30
• The sin, cos, and tan functions. – RK01 Jul 17 '15 at 12:32
• but $\sin$ $\cos$ can not be written as a fraction and $$\tan(x)=\frac{\sin(x)}{\cos(x)}$$ i don't understand your question – Dr. Sonnhard Graubner Jul 17 '15 at 12:38
• Can you give an example of an input that you'd want a "fractional answer" to? – Omnomnomnom Jul 17 '15 at 12:38
• or do you meant $\sin^{-1}(x)$? – Dr. Sonnhard Graubner Jul 17 '15 at 12:39

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.
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.