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How to Put Cis in Calculator

Reviewed by Calculator Editorial Team

The term "cis" in calculators refers to the cis function, which is used in complex number calculations. This guide explains how to properly input and use cis in scientific calculators, programming environments, and mathematical software.

What is cis in Calculators?

The cis function is a shorthand notation in mathematics for representing complex numbers in polar form. It stands for "cosine plus i sine" and is defined as:

cis(θ) = cos(θ) + i sin(θ)

Where:

  • θ (theta) is the angle in radians
  • i is the imaginary unit (√-1)
  • cos(θ) is the cosine of the angle
  • sin(θ) is the sine of the angle

The cis function is particularly useful in:

  • Complex number calculations
  • Electrical engineering
  • Quantum mechanics
  • Signal processing
  • Control systems

Note: Most scientific calculators don't have a built-in cis function, but you can calculate it using the cosine and sine functions separately.

How to Input cis in a Calculator

Since most standard calculators don't have a direct cis function, you'll need to calculate it using the cosine and sine functions. Here's how to do it:

Step-by-Step Guide

  1. Enter the angle value in radians
  2. Calculate the cosine of the angle
  3. Calculate the sine of the angle
  4. Multiply the sine result by i (the imaginary unit)
  5. Add the cosine and sine results together

Remember: Calculators typically use degrees by default. Make sure to set your calculator to radians mode for accurate cis calculations.

Using Programming Languages

In programming languages like Python, MATLAB, or JavaScript, you can use the cis function directly:

Python example:

import cmath
theta = 1.5708  # 90 degrees in radians
result = cmath.exp(1j * theta)  # Equivalent to cis(theta)

Using Graphing Calculators

On graphing calculators like TI-84 or Casio fx-CG50:

  • Set the mode to radians
  • Enter the angle in the calculator
  • Calculate cos(angle) + i*sin(angle)

Examples of cis in Calculators

Let's look at some practical examples of using cis in calculators:

Example 1: 30 Degrees

For θ = 30° (π/6 radians):

cis(π/6) = cos(π/6) + i sin(π/6)

= √3/2 + i (1/2)

Example 2: 45 Degrees

For θ = 45° (π/4 radians):

cis(π/4) = cos(π/4) + i sin(π/4)

= √2/2 + i (√2/2)

Example 3: 90 Degrees

For θ = 90° (π/2 radians):

cis(π/2) = cos(π/2) + i sin(π/2)

= 0 + i (1)

= i

These examples show how the cis function represents complex numbers on the unit circle in the complex plane.

FAQ

What is the difference between cis and exp?
The cis function is equivalent to e^(iθ) where e is Euler's number and i is the imaginary unit. Both represent complex numbers in polar form, but cis is often used in engineering contexts.
Can I use degrees instead of radians with cis?
No, the cis function always uses radians. If you have an angle in degrees, you must first convert it to radians before using cis.
Is cis the same as polar form?
Yes, cis(θ) is a shorthand notation for representing complex numbers in polar form, where θ is the angle and the magnitude is 1.
Where is the cis function used in real life?
The cis function is used in electrical engineering for phasors, in quantum mechanics for wave functions, and in signal processing for frequency analysis.