17Calculus Precalculus - Trigonometry
17Calculus
All of trigonometry is based on right triangles with the help of the unit circle. We have found some great sites and videos that explain trig intuitively and have lots of examples.
We do not attempt to cover all of trigonometry, just what you need for calculus.
FAQ: Do I need to take trigonometry before precalculus/calculus?
Short Answer: No, you do not NEED to take trig for Calculus 1 but you DO need it if you are going on to Calculus 2.
Long Answer: We highly recommend that you take trig before precalculus and calculus 1 but everything you need to know about trig can be learned in precalculus.
Without a full trig course, you can still use trig but it will be more work and you may not completely understand what is going on as well. Whether you decide to take trig or not is up to you and how much work you want to put into precalculus and later in calculus.
So, if you are self-motivated, you can learn all the trig you need for calculus 1 in this app.
So Why Take Trig?
In a full semester trigonometry course you learn the same concepts that we discuss here, but you get lots of extra practice with the trig functions, which increases your intuitive understanding of the unit circle and using the trig functions.
Additionally, if you are going on to calculus 2, you DO need to take trig because you learn a lot more than just the basics of trig. You also learn more about inverse trig functions, identities and laws that are critical to calculus 2, which you use for polar coordinates and vectors.
Extra Trig Topics - Time Not Wasted
Some trig courses also discuss complex numbers, which we do not use in calculus (1, 2 or 3). However, it is great practice using trig and will help you when you work with polar coordinates and vectors in calculus 2 and cylindrical and spherical coordinates in calculus 3.
Also, conics may be touched on in a trig course. This gives you a head-start on conics that you will study in calculus 2.
Bottom Line: If you take trig, you will better understand calculus and your calculus grades will probably be higher.
Recommended Books on Amazon (affiliate links) | ||
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A lot of what they teach in trigonometry is not directly used in calculus. That is to say, they have you work a lot problems in order to become comfortable with trig but the problems do not directly apply to calculus. That said, trig IS REQUIRED for calculus. However, this video playlist will go over most of the trig that you need calculus. This is a great series of videos that will help to refresh your memory or give you an idea of what trig you need to know for calculus.
James Hamblin - crash course trigonometry youtube playlist
video by James Hamblin |
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Intuitive Understanding of Trig
It is easy to get lost in the details of trig and never figure out why we are even learning it. BetterExplained.com has a great page on understanding trig intuitively. This page will give you a feel for it and some great examples on where trig is used and why we should study it. Before going on, read and study this page thoroughly.
Okay, now that you have an intuitive understanding of trig, let's talk specifics. Most of trig involves right triangles. So your next stop is the Right Triangles page.
Really UNDERSTAND Precalculus
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Topics You Need To Understand For This Page |
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Links |
Documents You May Find Helpful |
Pauls Online Notes - Trig Formula Sheets - Reduced (2 pages) |
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