If there is one prayer that you should pray/sing every day and every hour, it is the LORD's prayer (Our FATHER in Heaven prayer)
It is the most powerful prayer. A pure heart, a clean mind, and a clear conscience is necessary for it.
- Samuel Dominic Chukwuemeka

For in GOD we live, and move, and have our being. - Acts 17:28

The Joy of a Teacher is the Success of his Students. - Samuel Dominic Chukwuemeka

# Trigonometry/Triangles Calculators

I greet you this day,
Please solve the questions on your own before checking your answers with the calculators.
I wrote the codes for some of the calculators using JavaScript, a client-side scripting language.
The Wolfram Alpha widgets (many thanks to the developers) were used for some calculators.
Comments, ideas, areas of improvement, questions, and constructive criticisms are welcome. You may contact me.
If you are my student, please do not contact me here. Contact me via the school's system.
Thank you for visiting.

Samuel Dominic Chukwuemeka (Samdom For Peace) B.Eng., A.A.T, M.Ed., M.S

## Calculators for Triangles

### Right Triangles

• Given: Height, Base
To Find: Hypotenuse, Area, Perimeter

• Given: Height, Hypotenuse
To Find: Base, Area, Perimeter

• Given: Base, Hypotenuse
To Find: Height, Area, Perimeter

• Given: Area, Perimeter
To Find: Hypotenuse, Base, Height

OR

OR

### Triangles

Please NOTE: As applicable, all angles are in degrees.
If your angle is in radians, use this calculator to convert it to degrees.

• Given: $ASA$ (Common Side of Two Angles)
Sine Law is used
To Find: other details

$^\circ$

$^\circ$

• Given: $SAA$ (Uncommon Side of Two Angles)
Sine Law is used
To Find: other details

$^\circ$

$^\circ$

• Given: $SSA$ (Angle is non-included) - Ambiguous Case
Sine Law is used
To Find: other details

$^\circ$

• Given: $SAS$ (Angle is included)
Cosine Law is used
To Find: other details

$^\circ$

• Given: $SSS$
Cosine Law is used
To Find: other details

• Given: Three Sides
Hero's Formula (Heron's Formula) is used to find the area.
To Find: Perimeter, Area

## Calculators for Arcs, Sectors, Segments, and Chords

### Arcs

Please NOTE: Due to the rounding of the JavaScript Math.PI value, I used $\pi$ as $\dfrac{22}{7}$ rather than the Math.PI function.

• Given: Radius, Angle (in degrees)
To Find: Length of Arc

$^\circ$

OR $\pi$

• Given: Radius, Length of Arc
To Find: Angle (in degrees)

Please use only one field and Reset after each calculation
OR $\pi$

$^\circ$

• Given: Angle (in degrees), Length of Arc

$^\circ$

Please use only one field and Reset after each calculation
OR $\pi$

To Find: Length of Arc

Please use only one field and Reset after each calculation
RAD OR $\pi$

OR $\pi$

• Given: Radius, Length of Arc
To Find: Angle (in radians)

Please use only one field and Reset after each calculation
OR $\pi$

RAD OR $\pi$

• Given: Angle (in radians), Length of Arc

Please use only one field and Reset after each calculation
RAD OR $\pi$

Please use the corresponding one field and Reset after each calculation
OR $\pi$

• Given: Radius, Area of Sector
To Find: Length of Arc

• Given: Length of Arc, Area of Sector

### Sectors

Please NOTE: Due to the rounding of the JavaScript Math.PI value, I used $\pi$ as $\dfrac{22}{7}$ rather than the Math.PI function.

• Given: Radius, Angle (in degrees)
To Find: Area of Sector

$^\circ$

OR $\pi$

• Given: Radius, Area of Sector
To Find: Angle (in degrees)

Please use only one field and Reset after each calculation
OR $\pi$

$^\circ$

• Given: Angle (in degrees), Area of Sector

$^\circ$

Please use only one field and Reset after each calculation
OR $\pi$

To Find: Area of Sector

Please use only one field and Reset after each calculation
RAD OR $\pi$

OR $\pi$

• Given: Radius, Area of Sector
To Find: Angle (in radians)

Please use only one field and Reset after each calculation
OR $\pi$

RAD OR $\pi$

• Given: Angle (in radians), Area of Sector

Please use only one field and Reset after each calculation
RAD OR $\pi$

Please use the corresponding one field and Reset after each calculation
OR $\pi$

• Given: Radius, Length of Arc
To Find: Area of Sector

• Given: Area of Sector, Length of Arc

## Calculators for Bearings

### Bearings

• Given: Bearing of Point B from Point A
To Find: Bearing of Point A from Point B

$^\circ$

$^\circ$

• Given: Bearing
To Express: as a Compass Bearing

$^\circ$

$^\circ$

• Given: Bearing of Point B from Point A
To Express: Bearing of Point A from Point B as a Compass Bearing

$^\circ$

$^\circ$

• Given: Bearing of Point B from Point A (Conventional Representation)
To Express: Bearing of Point A from Point B as a Compass Bearing

$^\circ$

$^\circ$

## Calculators for Trigonometric Expressions

### Simplify Trigonometric Expressions

The calculator is a widget from Wolfram Alpha.
I tested it with some of the questions. It displayed at least one correct answer that I wanted, for some of the questions tested with it.
Hence, I put the widget on my website. You may check "most" of my solved examples with the calculator. At least one of its' answers to some of the questions is my solution.
The calculator is free. Please contact me if you see otherwise.
Thank you.

To use the calculator, please:
(1.) Type your expression in the textbox (the bigger textbox).
(2.) Type it according to the examples I listed. You may use $\theta$ or $x$
(3.) Delete the "default" expression in the textbox of the calculator.
(4.) Copy and paste the expression you typed, into the small textbox of the calculator.
(5.) Click the "Submit" button.
(6.) Check to make sure that it is the correct expression you typed.
(7.) Review the answers.

• Using the Trigonometric Expressions Calculator
• There may be several answers. At least one of the answers is what I needed.
• All outputs/answers are written as both integers and/or decimals; and integers and/or fractions.
• Delete the "default" expression in the textbox of the calculator.
• Type your expression in the bigger textbox first. Then, copy and paste it in the textbox of the calculator.
• Type: $\sin(-\theta) + \cos(-\theta)$ as sin(-theta) + cos(-theta) OR sin(-x) + cos(-x)
• Type: $\cos \theta \sin \theta(\tan \theta + \csc \theta)$ as cos(theta) * sin(theta)(tan(theta) + csc(theta))
• Type: $\dfrac{1}{1 + \cos \theta} + \dfrac{1}{1 - \cos \theta}$ as (1 / (1 + cos(theta)) +(1 / (1 - cos(theta))
• Type: $\dfrac{3\sin^2 \theta + \sin \theta - 10}{\sin \theta + 2}$ as (3sin^2(theta) + sin(theta) - 10) / (sin(theta) + 2)
• Type: $\dfrac{\sin^2 \theta - 25}{2\cos \theta + 1} * \dfrac{4\cos \theta + 2}{5\sin \theta + 25}$ as ((sin^2(theta) - 25) / (2cos(theta) + 1)) * ((4cos(theta) + 2) / (5sin(theta) + 25))
• Type: $\dfrac{8\cot \theta \csc \theta - 2\csc \theta}{4\cot \theta \csc \theta + 2\csc \theta}$ as (8cot(theta)csc(theta) - 2csc(theta)) / (4cot(theta)csc(theta) + 2csc(theta))
• Type: $\dfrac{(\cos \theta - \sin \theta)(\cos \theta - \sin \theta) - 1}{\sin \theta \cos \theta}$ as ((cos(theta) - sin(theta))(cos(theta) - sin(theta)) - 1) / (sin(theta)cos(theta))
• Type: $\sin \theta(\sin \theta - 2\cos \theta) + \cos^2 \theta$ as sin(theta)(sin(theta) - 2cos(theta)) + cos^2(theta)
• Type: $\tan^3 \theta + 27$ as tan^3(theta) + 27
• Type: $\dfrac{3 \sec \theta}{\csc \theta} + \dfrac{4\sin \theta}{\cos \theta}$ as (3sec(theta) / csc(theta)) + (4sin(theta) / cos(theta))

Simplify

## Calculators for Trigonometric Equations

### Solve Trigonometric Equations

The calculator is a widget from Wolfram Alpha.
I tested it with some of the questions. It displayed the correct answers for the questions I tested with it.
Hence, I put the widget on my website. You may check my solved examples with the calculator.
The calculator is free. Please contact me if you see otherwise.
Thank you.

To use the calculator, please:
(1.) Type your equation in the textbox (the bigger textbox).
(2.) Type it according to the examples I listed. You may use $\theta$ or $x$
(3.) Delete the "default" expression in the textbox of the calculator.
(4.) Copy and paste the equation you typed, into the small textbox of the calculator.
(5.) Click the "Submit" button.
(6.) Check to make sure that it is the correct equation you typed.
(7.) Review the solutions. There are usually several solutions. The solutions are given in radians.
(8.) Depending on your question, for $[0, 2\pi]$ range; test each solution for at least the two smallest values of $n$; when $n = 0$ and when $n = 1$.
(9.) Test for other solutions as necessary. Then, convert the solutions to degrees as necessary.

• Using the Trigonometric Equations Calculator
• There may be several answers. At least one of the answers is what I needed.
• All outputs/answers are written as both integers and/or decimals; and integers and/or fractions.
• Delete the "deafult" expression in the textbox of the calculator.
• Type your expression in the bigger textbox first. Then, copy and paste it in the textbox of the calculator.
• Type: $\sin(-\theta) + \cos(-\theta)$ as sin(-theta) + cos(-theta) OR sin(-x) + cos(-x)
• Type: $\cos \theta \sin \theta(\tan \theta + \csc \theta)$ as cos(theta) * sin(theta)(tan(theta) + csc(theta))
• Type: $\dfrac{1}{1 + \cos \theta} + \dfrac{1}{1 - \cos \theta}$ as (1 / (1 + cos(theta)) +(1 / (1 - cos(theta))
• Type: $\dfrac{3\sin^2 \theta + \sin \theta - 10}{\sin \theta + 2}$ as (3sin^2(theta) + sin(theta) - 10) / (sin(theta) + 2)
• Type: $\dfrac{\sin^2 \theta - 25}{2\cos \theta + 1} * \dfrac{4\cos \theta + 2}{5\sin \theta + 25}$ as ((sin^2(theta) - 25) / (2cos(theta) + 1)) * ((4cos(theta) + 2) / (5sin(theta) + 25))
• Type: $\dfrac{8\cot \theta \csc \theta - 2\csc \theta}{4\cot \theta \csc \theta + 2\csc \theta}$ as (8cot(theta)csc(theta) - 2csc(theta)) / (4cot(theta)csc(theta) + 2csc(theta))
• Type: $\dfrac{(\cos \theta - \sin \theta)(\cos \theta - \sin \theta) - 1}{\sin \theta \cos \theta}$ as ((cos(theta) - sin(theta))(cos(theta) - sin(theta)) - 1) / (sin(theta)cos(theta))
• Type: $\sin \theta(\sin \theta - 2\cos \theta) + \cos^2 \theta$ as sin(theta)(sin(theta) - 2cos(theta)) + cos^2(theta)
• Type: $\tan^3 \theta + 27$ as tan^3(theta) + 27
• Type: $\dfrac{3 \sec \theta}{\csc \theta} + \dfrac{4\sin \theta}{\cos \theta}$ as (3sec(theta) / csc(theta)) + (4sin(theta) / cos(theta))

Simplify

## TI-84 Graphing Calculator

### Make a Table of Values, Graph and Trace Functions Using the TI-84 Calculator

This calculator will:
(1.) Form a Table of Values.
(2.) Graph equations/functions.
(3.) Trace functions.
(4.) Displays the Table of Values and the Graph in the same window.

To use the calculator, please:
(1.) Visit the link:
(2.) Click the "Graphing" folder.
(3.) Click the link of "whatever you want to do".
(4.) Follow the directions as illustrated by the "blinking light".