## Trigonometry Calculator

Trigonometry, which studies the measure of triangles, takes algebra to the next level. Its most well-known features include the Pythagorean Theorem and the sine, cosine, and tangent ratios. Our trig calculator can help you check problems that involve these relationships as well as many others. Simply enter your problem into this advanced calculator to see if you worked it correctly.

Note: Mathway is available to assist you by showing you step by step how to work each problem you put into the calculator. If you cannot find your mistake, this is definitely the tool for you. Simply click View Steps in the answer screen to sign up.

Not only can this advanced calculator check answers but it can also provide additional practice problems to help hone your skills in preparation for tests and quizzes. To use this feature, find the type of problem you want to practice in the Examples section. Click on the desired topic, and an example problem will appear in the calculator screen. Click the Show button to see the problem in its standard format or as a picture if applicable. Solve the problem and click Answer to see if you are right.

Quick Trig Facts

### Pythagorean Theorem

$\large c^2 = a^2 + b^2$

### Trig Ratios

$\large \sin \theta \frac{opp}{hyp}$

$\large \cos \theta \frac{adj}{hyp}$

$\large \tan \theta \frac{opp}{adj}$

### Law of Sines

$\large \frac {a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$

### Law of Cosines

$\large c^2 = a^2 + b^2  2ab \cos C$

### Reference Triangles

Trigonometry Tips
• *Know your formulas: Investing the time to learn the formulas, definitions, and patterns will definitely pay off. That way, when you approach a problem, you will have the tools you need in order to solve it. Otherwise, you may get confused, and your work can quickly digress into a jumbled mess. You can use memory tricks such as SOH CAH TOA to help you. SOH CAH TOA is a memory aid for the trig ratios. SOH stands for Sine = Opposite over Hypotenuse, COH means Cosine = Adjacent over Hypotenuse and TOA helps you remember that Tangent = Opposite over Adjacent.
• *Take your time: As you progress into more advanced studies of mathematics, the problems become longer and more involved. Don’t let this intimidate you, and don’t be in a hurry to get done. Carefully and methodically work through each problem step by step, and you’ll eliminate a lot of careless errors.
• *Check your answers: It doesn’t do much good to practice if you’re practicing wrong, so check your answers to make sure you’re on the right track. Our calculator will help you with your homework, but if you have time you also want to go back and check your answers on tests and quizzes. You’ll be surprised how many mistakes you’ll catch and how many points this will save you.
• *Identify your errors: Many students end up making the same mistakes over and over again because they don’t pay attention to what went wrong when they miss a question. Mistakes are part of the learning process, but you have to identify and correct them. Every time you get a problem wrong, diligently search for your mistake and figure out what you should have done instead. If you can’t find your error, ask a teacher or friend for help. Or, sign up for Mathway, which will show you the steps to solve any problem you enter into the calculator.
How to Use the Calculator

1. Enter the problem into the calculator either by starting with an example or by using the symbols.
2. Click the Show button next to Math Format to ensure that you have entered your problem correctly. If it looks wrong and you need more help, click the ? box next to the Enter Problem field.
3. Under the Select Topic dropdown, choose the correct option for the type of problem you are trying to solve.

Starting with an Example
Scroll through the topics to find the type of problem you want to check or practice. This will provide an example in the calculator so that you can see how it is formatted. You can then change the numbers or variables to fit the problem you are trying to check.
Trigonometry Calculator Symbol Guide

Parenthesis – They indicate multiplication or that the operation inside should be done first.

Brackets – Use brackets if you need a parenthesis within parenthesis – The brackets go on the outside as seen in this example: [3 + 2(10 -1)] ÷ 7.

Absolute Value – The absolute value tells how far away a number is from zero. It’s always the same number but positive. For example, |3| is 3 and |-3| is also 3.

Fractions – Type the numerator and denominator inside the parenthesis that will come up. To create a mixed number, delete the parenthesis and put a space between the whole number and the numerator of the fraction. For example, for 2¼ type 2 1/4.

Exponents – Type the base before the ^ symbol and the exponent in parenthesis. For example, 5^(2) for $5^2$ . Remember that the exponent tells how many times the base is multiplied by itself.

Subscripts – Your variable goes outside the bracket and the subscript goes inside. For example, x1 would be x[1].

Square Roots – Type the radicand (the number inside the square root symbol) inside the parenthesis. Square roots find what number times itself equals the radicand. For example, the square root of 49 is 7 because 7 * 7 = 49.

Other Roots – Type the index after the √ symbol and the radicand inside the parenthesis. For example, use √3:(8) for $\sqrt[3]{8}$ . Remember that a different index means that the answer must be multiplied by itself that many times to equal the radicand. In our $\sqrt[3]{8}$ example, 2 * 2 * 2 = 8, so 2 would be the answer because 2 times itself 3 (the index) times is 8.

Note: If no index is given, it is assumed to be two and is just called a square root.

Coordinates – Type a coordinate as you normally would – such as (1,5).

Greater than or equal to – If you need to use just the greater than sign ( > ), simply type it using your keyboard. (Hit shift then the period).

Less than or equal to – If you need to use just the greater than sign ( > ), simply type it using your keyboard. (Hit shift then the period).

Functional Notation – Type functional notation as you normally would. Remember that f(x) is pronounced “f of x” and typically replaces y in an equation.

Natural Logarithm – Type the number inside the parenthesis. Remember that a natural logarithm answers the following question: e to what power equals the given number? The constant e is approximately equal to 2.718.

Logarithm – Type the number inside the parenthesis. A logarithm with no subscript (such as the one seen here) answer the question “10 to what power equals the number given?” For example, the answer to log 100 is 2 because 10 to the 2nd power is 100.

Logarithm with a different base – Type the base (the small number) inside the brackets and the argument (the regularly sized number) inside parenthesis. For example, $\log_{2}8$ would be written as log[2](8). When you change the subscript number on a logarithm, you are changing the base. This example is asking the following: 2 to what power equals 8? The answer, of course, would be 3.

Note: If no subscript (base) is given, the base is assumed to be 10.

Right Triangles – Enter the information you have within the brackets. Be sure to use the correct order, which is as follows: [angle, 90°, angle, leg, leg, hypotenuse]. Click Show to double-check that you have entered your information into the appropriate place.

Sine – Type the measure of the angle inside the parenthesis. The sine of an angle is the opposite over the hypotenuse.

Cosine – Cosine equals adjacent over hypotenuse.

Tangent – Tangent is opposite over adjacent.

Secant – Secant is the inverse of the cosine and is equal to hypotenuse over adjacent.

Cosecant – The cosecant is found by inverting the sine and is equal to hypotenuse over opposite.

Cotangent – The cotangent, the inverse of the tangent, is found by placing the adjacent over the opposite.

Division sign – For multiplication, use the asterisk button on your keyboard. (Hit shift then 8.)

Pi – Pi is a unique number that is found by dividing the circumference of any circle by its diameter. Pi is approximately equal to 3.14.

Degrees – Use the degree symbol when needed to indicate degrees.

Theta – The Greek letter Theta is used in trigonometry to represent an unknown angle.