What is trigonometry?
I am sure that all of you know what 'triangle' is. Am I right? How can you define triangle?. Think. The word has reason to be. Tri-angle. Three angles! Triangle is a plane figure which has three angles (corners) and three sides (edges). then, what kind of triangles do you know already? List as much as you can come up with. Acute triangle, obtuse triangle, isosceles triangle, equaliteral triangle, right triangle. This page is about 'trigonometry'. Among these triangles, what is working with it?
Trigonometry uses right triangle, that one of its triangle is right angle (90º). Let's look at one example above. Triangle ABC is a right triangle that the angle C is a right angle. Let's call the angle B as theta(Θ) The hypotenuse is sigment AB, which is the opposite side of right angle and the longest among three sides, sigment BC is the adjacent, and sigment AC is the opposite side of angle B, Θ.
The first step of trigonometry is 'Pythagorean Theorem'. Square of hypothenus is the sum of the square of rest two sides. Or, h²=b²+p². You may saw 'a²=b²+c²' somewhere. It's same thing, just using different letters for same things. Then, from this theorem, you can find that the length of hypothenus is √(b²+h²).
Let's go to the next step. Did you ever see something like 'sin' and 'csc'? These represent trigonometric ratios. There are three major ones;
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sin (sine) = opposite/hypothenus
cos (cosine) = adjacent/hypothenus
tan (tangent) = opposite/adjacent
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What is sinΘ for this triangle? Sin is opposite over hypothenus, so segment AC over segment AB.
Inverse
Besides, there are something called secant, cosecant and cotangent. What are they? They are the inverse of sine, cosine and tangent.
Secant (sec) is the inverse of cosine (cos), so we can say secΘ=1/cosΘ.
Cosecant (csc or cosec) is the inverse of sine (sin), cscΘ=1/sinΘ.
Cotangent (cot) is the inverse of tangent (tan), cotΘ=1/tanΘ.
Cot is quite easy to memorize, but sec and csc must be confusing. Here is an easy way. See the third letter. Secant 'C', which is cosine, cosecant 'S', which is sine. When you just read, you might think you get it, but you have to practice to make it your own.
If you have anything that want me to explain more or if you have any questions, please leave it on this page.
Acute triangle | The triangle that its three angles are all acute angles. (smaller than 90º)
Obtuse triangle | The triangle that one of its angle is obtuse angle. (bigger than 90º and smaller than 180º)
isosceles triangle | The triangle that its two sides are same in length.
equaliteral triangle | The triangle that its three sides are all same and three angles are all same.
More about Pythagorean Theorem-
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