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How to Calculate Degrees and Complex Numbers in Ti84

Reviewed by Calculator Editorial Team

The TI-84 calculator is a powerful tool for performing mathematical calculations, including degree measurements and complex number operations. This guide will walk you through the essential steps for working with degrees and complex numbers on your TI-84.

Degree Calculations

Degrees are a common unit of measurement for angles. The TI-84 can perform various degree-based calculations, including trigonometric functions, angle conversions, and more.

Basic Trigonometric Functions

To calculate trigonometric functions in degrees:

  1. Press the MODE button to ensure the calculator is in degree mode (look for "Deg" in the display).
  2. Enter the angle in degrees.
  3. Press the appropriate trigonometric function button:
    • sin for sine
    • cos for cosine
    • tan for tangent
sin(θ) = opposite/hypotenuse cos(θ) = adjacent/hypotenuse tan(θ) = opposite/adjacent

Inverse Trigonometric Functions

To find the angle from a trigonometric ratio:

  1. Enter the ratio.
  2. Press the 2nd button, then the appropriate trigonometric function button:
    • 2nd sin⁻¹ for arcsine
    • 2nd cos⁻¹ for arccosine
    • 2nd tan⁻¹ for arctangent

Complex Numbers

Complex numbers are numbers that have both a real and an imaginary part. The TI-84 can perform operations with complex numbers, including addition, subtraction, multiplication, and division.

Entering Complex Numbers

To enter a complex number:

  1. Press the MODE button to ensure the calculator is in complex mode (look for "a+bi" in the display).
  2. Enter the real part of the number.
  3. Press the + button.
  4. Enter the imaginary part of the number.
  5. Press the i button.

Operations with Complex Numbers

To perform operations with complex numbers:

  1. Enter the first complex number.
  2. Press the operation button (+, -, ×, or ÷).
  3. Enter the second complex number.
  4. Press the = button to see the result.
(a + bi) + (c + di) = (a + c) + (b + d)i (a + bi) - (c + di) = (a - c) + (b - d)i (a + bi) × (c + di) = (ac - bd) + (ad + bc)i (a + bi) ÷ (c + di) = [(ac + bd) + (bc - ad)i] / (c² + d²)

Conversion Between Degrees and Radians

The TI-84 can convert between degrees and radians, which is useful for trigonometric calculations.

Converting Degrees to Radians

To convert degrees to radians:

  1. Enter the angle in degrees.
  2. Press the MODE button to ensure the calculator is in radian mode (look for "Rad" in the display).
  3. Press the × button.
  4. Enter the conversion factor (π/180).
  5. Press the = button to see the result in radians.

Converting Radians to Degrees

To convert radians to degrees:

  1. Enter the angle in radians.
  2. Press the MODE button to ensure the calculator is in degree mode (look for "Deg" in the display).
  3. Press the × button.
  4. Enter the conversion factor (180/π).
  5. Press the = button to see the result in degrees.
radians = degrees × (π/180) degrees = radians × (180/π)

Example Calculations

Example 1: Calculating sin(30°)

  1. Press MODE to ensure the calculator is in degree mode.
  2. Enter 30.
  3. Press sin.
  4. The result is 0.5.

Example 2: Adding Complex Numbers (2 + 3i) + (4 + 5i)

  1. Press MODE to ensure the calculator is in complex mode.
  2. Enter 2, then +, then 3, then i.
  3. Press +.
  4. Enter 4, then +, then 5, then i.
  5. Press =.
  6. The result is 6 + 8i.

Example 3: Converting 90° to Radians

  1. Enter 90.
  2. Press MODE to ensure the calculator is in radian mode.
  3. Press ×.
  4. Enter π (press 2nd, then π).
  5. Press ÷, then 180.
  6. Press =.
  7. The result is approximately 1.5708 radians.

FAQ

How do I change the angle mode on my TI-84?
Press the MODE button and use the arrow keys to select "Deg" for degrees or "Rad" for radians. The current mode is displayed at the bottom of the screen.
How do I enter a complex number on my TI-84?
Press the MODE button to ensure the calculator is in complex mode (look for "a+bi"). Then enter the real part, press +, enter the imaginary part, and press i.
Can I perform trigonometric calculations in radians on my TI-84?
Yes, press the MODE button to switch to radian mode before performing trigonometric calculations.
How do I convert between degrees and radians on my TI-84?
Multiply degrees by π/180 to convert to radians, or multiply radians by 180/π to convert to degrees. Use the 2nd button to access π.
What should I do if I get an error when performing complex number calculations?
Ensure the calculator is in complex mode (check the display shows "a+bi"). Also, make sure you've entered the numbers and operations correctly.