# Trig for Calculus-Based Physics: What's Used?

• starchild75
In summary, trigonometry is essential in physics, particularly in topics such as Newtonian mechanics and projectile motion. Basic trigonometric concepts like SOH CAH TOA and vector methods are used, as well as the law of sines and law of cosines in certain calculations. Trigonometry is also necessary for advanced topics such as AC circuits and integrals. While there may be different methods or acronyms used to learn trigonometry, it is important to have a thorough understanding of the concepts for success in physics.

#### starchild75

HI all!

I am going to be taking calculus-based physics next January and I am taking trig right now. My question is, how much of trig is used in the first couple physics classes? Is it simply SOH CAH TOA, or are proofs, law of sines, etc. used?

Thanks,

Starchild

You'll probably end up doing some Newtonian mechanics, which uses trig. Trig is used to resolve the components of forces (don't worry if you don't know what this means yet). For projectile work and some other stuff, you'll be resolving forces at right angles, so it's just your basic 'sohcahtoa'. There will be some forces work though in which it's useful to know the sine and cosine rules. You might be able to get away with not knowing the rules by just using a petractor and a ruler, though I personally find this too fiddly.

Either way, keep learning trig! It's really interesting and very helpful too.

Trig is used throughout. Knowing the law of sines and the law of cosines would be helpful... but it is essential that you fully understand SOH CAH TOA and various vector methods.

starchild75 said:
HI all!

I am going to be taking calculus-based physics next January and I am taking trig right now. My question is, how much of trig is used in the first couple physics classes? Is it simply SOH CAH TOA, or are proofs, law of sines, etc. used?

Thanks,

Starchild

Trigonometry is indispensable in physics. Your first semester, such things as SOHCAHTOA will be very helpful to you. By second semester, setting up certain integrals will require a bit more trigonometric intuition. The Law of Cosines is used to compute the gravitational field of a spherical shell (and in certain other calculations), but there's no need to memorize it. And fortunately, there are never any mathematical proofs in physics.

Definitely pay attention in trig, because this stuff will serve you well next year!

You should definitely know your trigonometry and geometry I guess. From my experience it seems that most students, including me, don't remember much of their trig or geometry. Luckily I do my HW in my schools math and engineering library, so trig and geometry textbook is always close by.

And if you decide to take any circuit analysis courses that include AC circuits, prepare for a lot of trig, particularly when the AC power analysis comes around. I think second semester calc will adequately prepare most to deal with the trig after navigating through some trig substitution integrals. Its just when you need this or that identity, you would swear that the teacher has them all memorized when in truth it is in front of them on their notes, but if they don't act like they know it then how can they ever expect you to? Anyway, (kill.rant;)

SOH CAH TOA is the worst way to learn trigonometry. You won't be able to understand physics if you don't understand trigonometry thoroughly, and that implies not using acronyms.

Werg22 said:
SOH CAH TOA is the worst way to learn trigonometry. You won't be able to understand physics if you don't understand trigonometry thoroughly, and that implies not using acronyms.

Respectfully, I would disagree. Back in sixth grade this is how I learned basic trigonometry, and it proved to be very useful until I took algebra 2 in high school. Eventually everyone should learn the coordinate geometric definition (i.e. the one that utilizes the unit circle). But to this day I often use the more basic definition to gain an intuitive grasp when solving problems in physics.

Of course I've used the definitions so much that I no longer need to remember the acronym.

In my experience, there is no such thing as "useless mathematics" when you're dealing with physics. I'm still using trig identities/referencing trigonometric identities every day and I'm a graduate student. I'm sure the professionals on this forum would agree with me.

StatMechGuy said:
In my experience, there is no such thing as "useless mathematics" when you're dealing with physics. I'm still using trig identities/referencing trigonometric identities every day and I'm a graduate student. I'm sure the professionals on this forum would agree with me.

Well I'm not a professional, but I'll be a grad student next Fall (in physics), so I'm in the same boat as you. I agree with you, I too have found a use for most of the mathematics I learned. I think the only exception would be the rigorous proofs that are associated with professional mathematics. I guess we physicists don't use those too often, but it's nice to know that all of our smarmy tricks are logically justifiable.

I understand trigonometry very well. I am doing well in my class. I was only asking how much trigonometry is used in physics. I don't think it's fair to assume I don't understand trig because I used acronyms in this particular post.

Respectfully,

Starchild

SolarisOne
Some examples of (basic) trigonometry in physics could be:

Force resolutes - FgCos(Theta)
Addition of Sine waves - Sine(X+Y), used in electronics
Oscillations
etc

There's much, much more than that, but that's some applicable examples for you.

Knowing your trig identities are helpful. For a first semester physics most of your trig will go into finding vector components and setting up problems more than anything else, but knowing your identities is very useful when doing integration (especially when learning work and energy).

## 1. What is trigonometry used for in calculus-based physics?

Trigonometry is used to study the relationships between the sides and angles of triangles. In calculus-based physics, it is used to analyze and solve problems involving angles, velocity, acceleration, and oscillations.

## 2. How does trigonometry relate to vectors in physics?

Trigonometry is essential for understanding and working with vectors in physics. It is used to find the components of a vector, calculate its magnitude and direction, and perform operations such as addition and subtraction.

## 3. Can you give an example of a trigonometric function used in physics?

One example of a trigonometric function used in physics is the sine function. It is used to describe the relationship between the angle of a pendulum and its period of oscillation.

## 4. Do I need to have a strong understanding of trigonometry to excel in calculus-based physics?

Yes, a strong understanding of trigonometry is crucial for success in calculus-based physics. Many concepts, such as kinematics, dynamics, and oscillations, rely heavily on trigonometric principles.

## 5. How can I improve my trigonometry skills for calculus-based physics?

Practice is the key to improving trigonometry skills for calculus-based physics. Make sure to review basic trigonometric identities and formulas and work through practice problems to strengthen your understanding of how to apply them in physics contexts.