# Requirements for learning and understanding trigonometry?

Im reaching a point in programing where I need to create basic shapes which I simply cant since my math skills are very bad. After finding out that the skills required are trigonometry I read a few books. The result was that I couldnt understand any word at all.

What is required in order to understand basic 2D and 3D trigonometry? Calculus? Algebra? Also how long in general would it take for an average person to learn the material. It would be great if you could give me a guide for someone like me who only knows adding, multiplication, division and substracting.

• Usually just a thorough understanding of algebra is needed. It is Taught, along with advanced algebra in a class called precalculus in most high schools. In the United States, at least. – Shinaolord Apr 15 '15 at 16:03
• "Thorough understanding of algebra" is an exaggeration. A person with only some pretty basic algebra who understands what proofs are can learn how to show that $\sin(\alpha+\beta)=\sin\alpha\cos\beta+\cos\alpha\sin\beta$ or how to tell what the graphs of trigonometric functions look like or how to solve triangles or how to derive things like the identity for the tangent of a sum from the identity for the sine of a sum, etc. ${}\qquad{}$ – Michael Hardy Apr 15 '15 at 16:08
• @Michael Hardy True, but by thorough, I meant that you shouldn't be iffy with your ability to manipulate equations with letters, sometimes multiple letters. If you have difficulty with that, which is essentially the cornerstone of algebra one, then you're pretty much going to have a very difficult time in trigonometry. – Shinaolord Apr 15 '15 at 16:21
• +1 for the question. @user57404 : Geometry is conspicuously not mentioned in your comment. ${}\qquad{}$ – Michael Hardy Apr 15 '15 at 16:22
• @Michael Hardy True, geometry is important as well. But the majority of geometry focuses on everything except triangles, which isn't of extreme help, especially not nearly as much as algebra is. This is of course my opinion. – Shinaolord Apr 15 '15 at 16:24

You certainly do not need calculus. You need some basic algebra. There are a few things in basic geometry that you show be thoroughly aware of:

• The number $\pi$ is the ratio of circumference to diameter of a circle. For example, a circle whose diamater is $1$ foot has a circumference of $\pi$ feet, i.e. about $3.14159\ldots$ feet. And $2\pi$ is the ratio of circumference to radius, so if the radius is $1$ foot (and thus the diameter is $2$ feet) then the circumference is $2\pi$ feet.
• There are $90^\circ$ in a right angle, and $180^\circ$ in a straight angle.
• The sum of the angles in every triangle is $180^\circ$. There are easy geometric arguments showing why that is so. You show learn to understand those arguments.
• An isoceles triangle is one in which two sides have equal lengths. You should know that that happens if, and only if, the measures of the angles opposite those two sides are equal.
• In particular, an isoceles right triangle, i.e. an a triangle with one right angle and two smaller angles whose measures are equal to each other, must have two $45^\circ$ angles. That that must be so is a logical consequence of things said above, and you should learn to understand why it is their logical consequence.
• Also as a consequence of other things above, a triangle is equilateral, i.e. its three sides all have equal lengths, if, and only if, its three angles are equal. You should understand how the points above logically entail that and how they entail that in that case, the angles must be $60^\circ$ each.
• You should know how to explain what the Pythagorean theorem says without saying anything that sounds like "A squared plus B squared equals C squared". It says: The sum of the areas of the squares on the legs of a right triangle equals the area of the square on the hypotenuse. It's about areas of squares, not just about multiplying each of three numbers by itself. Learn how to prove that and how to use it.
• I feel as though you neglected some more advanced algebra concepts that are needed, but I suppose those can be taught along with the trigonometry course. Plus one for the answer, which reminds me that there is a lot of basics about triangles you do learn in geometry, that I thought were covered in middle school – Shinaolord Apr 15 '15 at 16:27
• Regardless of whether they're covered in middle school, they are examples of geometry. ${}\qquad{}$ – Michael Hardy Apr 15 '15 at 16:32
• True. I withdraw. – Shinaolord May 13 '15 at 21:08

I am useing Khan academy to catch up on things I have hut the algebra 1 and 2 sections so I am going to learn liner and diffrential algebra before I go back to the algebra 1 and 2 sections, but when I am doing liner algebra I have noticed like the Pythagorean theorem is in the geometry section and some of the algebra sums deal ing geometry and trigometry sections, so I might just go sstudy geometry and trigomety then go back to liner, diffrential and algebra 1 and 2 sections before moving onto pre calculus and calculus sections because I whant to build a solid foundation of things before going to the calculus sections.