Login
Copyright

Math Review for Physics: Trigonometry

An error occurred trying to load this video.

Try refreshing the page, or contact customer support.

Coming up next: Elements of the SI: Base & Derived Units

You're on a roll. Keep up the good work!

Take Quiz Watch Next Lesson
 Replay
Your next lesson will play in 10 seconds
  • 0:00 Trigonometry in Physics
  • 0:42 Pythagorean Theorem
  • 1:23 Trigonometric Functions
  • 3:11 Inverse Trigonometric…
  • 4:30 Lesson Summary
Add to Add to Add to

Want to watch this again later?

Log in or sign up to add this lesson to a Custom Course.

Login or Sign up

Timeline
Autoplay
Autoplay
Create an account to start this course today
Try it free for 5 days!
Create An Account
Lesson Transcript
Instructor: Damien Howard

Damien has a master's degree in physics and has taught physics lab to college students.

This lesson reviews some basic trigonometry that is essential for an introductory physics course. Here we'll focus on the various methods for finding side lengths and angle measurements of a right triangle.

Trigonometry in Physics

When you're working a physics problem, you are often dealing with a complex situation involving people, places, and things interacting with one another. In order to try to make sense of these situations, you can draw diagrams to understand what is going on in a physics problem. Some of the first diagrams you'll create will be for motion in two dimensions, and here you'll notice that right triangles show up quite a lot. In order to solve problems like these you'll need to know some trigonometry. In fact, you'll find you need trigonometry not just for 2-dimensional motion problems, but for many places in physics.

Pythagorean Theorem

One of the most basic and essential things you will do with trigonometry is find the various side lengths and angle measurements of a right triangle. You can go about this in multiple ways, but one of the first ways you would have learned in a trigonometry course is known as the Pythagorean theorem, which is defined as:

a^2 + b^2 = c^2

The variables, a, b, and c are the three side lengths of a right triangle, where c is always the side opposite the right angle in the triangle. The Pythagorean theorem allows you to find the third side length of a triangle as long as you know the other two.

Trigonometric Functions

What if you only know one side length of a triangle, though? Well, as long as you know one of the two angles other than the right angle in the triangle you can still find the lengths of all the triangle's sides. To do this you use the trigonometric functions. The most common three are known as sine, cosine, and tangent. Theta represents the angle you know.

  • sin(theta) = length of the opposite leg / length of the hypotenuse
  • cos(theta) = length of the adjacent leg / length of the hypotenuse
  • tan(theta) = length of the opposite leg / length of the adjacent leg

The hypotenuse is the side we called c in the Pythagorean theorem, and is always the side of the triangle across from the right angle. As their names suggest, the adjacent and opposite sides are the sides of the triangle adjacent and opposite to the non-right angle (theta) you are using.

These are the three trigonometric functions with which most people are familiar, but you might not know there are actually three more called cosecant, secant, and cotangent. Each of these three new trigonometric functions is actually the reciprocal of one of the previous functions we went over, where the reciprocal of any non-zero number or function is one divided by that same number or function.

  • csc(theta) = length of the hypotenuse / length of the opposite leg
  • sec(theta) = length of the hypotenuse / length of the adjacent leg
  • cot(theta) = length of the adjacent leg / length of the opposite leg

To unlock this lesson you must be a Study.com Member.
Create your account

Register for a free trial

Are you a student or a teacher?
I am a teacher

Unlock Your Education

See for yourself why 30 million people use Study.com

Become a Study.com member and start learning now.
Become a Member  Back

Earning College Credit

Did you know… We have over 95 college courses that prepare you to earn credit by exam that is accepted by over 2,000 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.

To learn more, visit our Earning Credit Page

Transferring credit to the school of your choice

Not sure what college you want to attend yet? Study.com has thousands of articles about every imaginable degree, area of study and career path that can help you find the school that's right for you.

Create an account to start this course today
Try it free for 5 days!
Create An Account
Support