C A L C U L A T O R

As I have mentioned in my earlier post, a calculator is required to solve trigonometric problems. 

Where the sine, cosine and tangent key can be found is shown below. 

To access the inverse sine, cosine or tangent key, press shift + the sine, cosine or tangent key.

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IN REAL L I F E

Trigonometry is actually quite relevant especially relating to real life situations. We often, however fail to foresee its importance as we refrain from thinking about its relevance.

Trigonometry is required in many career paths such as:

- architecture
- biology
- chemistry
- actuary
- animation
- astronomy
- attorney

and many more.

Trigonometry is commonly used in finding the height of towers and mountains.




It is used in finding the distance between celestial bodies.



The sine and cosine functions are fundamental to the theory of periodic functions such as those that describe sound and light waves.



Trigonometric identities are found heavily in architecture. especially when developing large infrastructure. The six different identities are used to find either the length of one one or more sides of a shape, or the angle at which different materials should be placed at. It is common to find them when constructing blueprints for actual structures. (Examples of this are shown below.) 




Trigonometric identities are applicable in the field of music for stringed instruments.  For example, the vibration of a violin possesses the same shape as a sine function. When playing instruments you don't think about trigonometric identities, but when calculating the physics behind it, they come into play. Trig identities in music are typically a calculation of frequency and are represented by using kilohertz (kHz) 

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T H E U N K N O W N

In order to find the unknown side or angle you must have a scientific calculator. Ensure that your scientific calculator is in degree mode.
To find the unknown side:

We first decide which of the trigonometric ratios must be used; In this problem we must use the sinθ ratio since the opposite side (O) and the hypotenuse (H) are involved.

We then multiply both sides by 41 and evaluate using the calculator.



sin 25° = x / 41

 x = 41 sin 25° 
      
    =17.33           





To find the unknown angle:

Just like finding out the unknown side we must first decide which of the trigonometric must be used; In this problem we must use the tanθ ratio since the opposite side (O) and the adjacent side (A) are given.

We then use the inverse tangent key on your calculator 

  
    
      tan θ = 16/22
       
      θ = 36.027.....°
      
      θ = 36°

- k.v.

B E A R I N G S

Bearings are used to indicate direction and therefore are commonly used to navigate the sea or air in ships or planes. Bush walkers use bearings with a compass to help follow a map and navigate a forest. The most common type of bearing is the true bearing measured clockwise from north.

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P Y T H A G O R A S

Pythagoras was born on the Greek island of Samos in the 6th century BC. He received a privileged education and traveled to Egypt and Persia where he developed his ideas in mathematics and philosophy. He settled in Crotone, Italy, where he founded a school. His many students and followers were called the Pythagoreans and under the guidance of Pythagoras, lived a very structured life with strict rules. 

The Pythagoreans discovered the famous theorem, which is named after Pythagoras, and the existence of irrational numbers, which cannot be written down as a fraction or a terminating decimal. Such numbers cannot be measured exactly with a ruler with fractional parts and were thought to be unnatural. The Pythagorans called these numbers 'unutterable' numbers and it is believed that any member of the brotherhood who mentioned these numbers in public would be put to death.

- k.v.