Trigonometry made easy

Trigonometry is a very interesting branch of mathematics that deals with the angle and side measurements of a right angled triangle. It demonstrates the relationship between sides and angles using very simple trigonometric equation. A lot of people when they hear the word trigonometry they get so scared saying its hard and complicated, but trust me they are missing out on the joy of understanding and loving trig functions!!!

First, in order to understand trig, you should know its basics!

Trig consists of three angles: \(Sin\), \(Cos\), and \(Tan\). What do these mean? Sin is the angle measured to the opposite side of the hypotenuse where \(sinx=opp/hyp\). Cos is the angle measured to the adjacent side of the hypotenuse where \(cosx=adj/hyp\). Tan is the opposite over the adjacent: \(tan=sin/cos=opp/adj\).

These identities can be used when given at least the measurement of one angle and one side, but what if there was no given angle and only 2 side measurements? This is when the Pythagorean Theorem comes into play! This theorem states that the square of hypotenuse is equal to the sum of the square of both sides. \(c^2=a^2+b^2\)

The Pythagorean Theorem relates to trig functions by the identity: \(cosx^2+sinx^2=1\).

What about if the triangle was not a right triangle? How can we determine the missing angle or side? Easy, using the \(sin\) or \(cos\) law!!

Sin law for triangle \(ABC\): \(sinA/a=sinB/b=sinC/c\) It is used when you have at least 2 knows sides and one angle, or 2 angles are one known side.

Cos law for triangle \(ABC\): \(c^2=a^2+b^2 2abcosc\) Used when the measurements of 2 sides and angle are given. The equation can be arranged according to what is being solved for angle or side.

Degrees and Radians: To convert from degrees to radians multiply by \(\frac{π}{180}\); to convert radians to degrees multiply by \(\frac{180}{π}\). Most common ones to know: degree \(0\), \(30\), \(45\), \(60\), \(90\), \(180\); radian \(0\), \(\frac{π}{6}\), \(\frac{π}{4}\), \(\frac{π}{3}\), \(\frac{π}{2}\), \(π\).

\(Sin\) and \(cos\) lie on the unit circle of radius 1. This is why there value is between 1 and -1. When graphing a sin or cos function the waves alternate between the values 1 and -1 only.

The other trig functions: \(csc\), \(sec\), and \(cot\): \(cscx=1/sinx\), \(secx=1/cosx\), \(cotx=1/tanx\).

Trig Identities: \(sin(x±y)=sinxcosy ± sinycosx\); \(cos(x±y)=cosxcosy±sinxsiny\).

Double angle formula: \(sin2x=2sinxcosx\); \(cos2x=cos^2⁡(x)-sin^2(⁡x)\).