Question

How do you find the secant, cosecant, and cotangent on a TI-83 calculator?

Answer 1

Hint: Secant, cosecant and cotangent (also known as sec, cosec and cot generally) are trigonometric functions. The sec function can be defined as the ratio of the length of the hypotenuse to that of the base in a right-angled triangle. Whereas, the cosec function can be defined as the ratio of the length of the hypotenuse to that of the perpendicular in a right-angled triangle. And, the cot function can be defined as the ratio of the length of the base to that of the perpendicular in a right-angled triangle.
These trigonometric functions, namely sec, cosec and cot are the reciprocal functions of cos, sin and tan (also known as cosine, sine and tangent) respectively. The relation between them is given below as trigonometric identities:
1. $\sec \theta ={\displaystyle \frac{1}{\cos \theta }}$
2. $\mathrm{cosec}\theta ={\displaystyle \frac{1}{\sin \theta }}$
3. $\cot \theta ={\displaystyle \frac{1}{\tan \theta }}$

Complete Step by Step Solution:
To find the value of $\sec$, $\csc$ and $\cot$ functions on a TI-83 calculator, firstly we will have to set up the mode of the calculator. For this,
1. Press MODE (which is just beside the bright yellow button).
2. Now for the information which appears on your screen, set the first line to Normal, the second line to Float, the third line to Radian, the fourth line to Func, the fifth line to Connected, the sixth line to Sequential, and the seventh line to Real.
Now since the TI-83 calculator does not have a built-in function to find the values of $\sec$, $\csc$, and $\cot$ trigonometric functions, therefore we will find them with the help of reciprocal trigonometric identities as mentioned above.
Let us assume we have to find the value of $\sec {\displaystyle \frac{\pi }{3}}$, $co\sec {\displaystyle \frac{\pi }{3}}$ and $\cot {\displaystyle \frac{\pi }{3}}$.
3. To find $\sec {\displaystyle \frac{\pi }{3}}$, Press 1, then $÷$ sign, then cos, then 2nd button (the bright yellow button), then $\pi$, then $÷$, then 3, then ), and finally press Enter. Below are only the buttons given in a sequential order:
$1\to ÷\to \cos \to 2^{nd}\to \pi \to ÷\to 3\to )\to Enter$
Or we can also press cos, then 2nd, then $\pi$, then $÷$, then 3, then ), then x-1, and enter. Simply,
$\cos \to 2^{nd}\to \pi \to ÷\to 3\to )\to x^{-1}\to Enter$
4. To find $co\sec {\displaystyle \frac{\pi }{3}}$, Press 1, then $÷$ sign, then sin, then 2nd button (the bright yellow button), then $\pi$, then $÷$, then 3, then ), and finally press Enter. Below are only the buttons given in a sequential order:
$1\to ÷\to \sin \to 2^{nd}\to \pi \to ÷\to 3\to )\to Enter$
Or we can also press sin, then 2nd, then $\pi$, then $÷$, then 3, then ), then x-1, and enter. Simply,
$\sin \to 2^{nd}\to \pi \to ÷\to 3\to )\to x^{-1}\to Enter$
5. To find $\cot {\displaystyle \frac{\pi }{3}}$, Press 1, then $÷$ sign, then tan, then 2nd button (the bright yellow button), then $\pi$, then $÷$, then 3, then ), and finally press Enter. Below are only the buttons given in a sequential order:
$1\to ÷\to \tan \to 2^{nd}\to \pi \to ÷\to 3\to )\to Enter$
Or we can also press tan, then 2nd, then $\pi$, then $÷$, then 3, then ), then x-1, and enter. Simply,
$\tan \to 2^{nd}\to \pi \to ÷\to 3\to )\to x^{-1}\to Enter$
Hence, by this way we can find the value of secant, cosecant, and cotangent on a TI-83 calculator.

Note:
To find the value of trigonometric functions in degrees, we can just simply change the third line to Degree when we press MODE (as given in the 2nd step).