There are various categories of triangles that you will read about in Mathematics. Each has three sides along with the angles within them. Students have to learn all the properties associated with the figure. In your exams, you will mainly have to measure different sides with the properties. In case one of these angles measures up to the value of 90, you can call it right-angled. It has a special side (hypotenuse) which is the longest and is opposite as well. In the field of trigonometry, this triangle is the base from which you get all the formulas. Without this, you won’t be able to apply the various identities as well.
The Major Importance
There are various fields where you can apply the knowledge of trigonometry. It makes it easier to calculate the distance between two locations as well. You don’t have to spend weeks measuring how tall a building or a mountain is. All you have to do is calculate the angle made by its shadow. Since you can get the sin or cosine of the angle, you can get the ratio directly. Once you know the length of the shadow, do the equation and you will get the value of the height.
Apart from this, it is used in geographical navigations as well. You can get the instant angle and altitude at which a plane is flying. When it comes to Electronics and other fields, trigonometry is the base subject. It allows you to derive some of the most important formulas in higher classes. The subject came into existence due to the discovery made by Hipparchus, a Greek Mathematician. Not only can you measure the sides but also get certain identities using trigonometry. The theorems and proofs are important for physicians who are into research.
The Basics You Need to Know
First, you need to draw a triangle where one angle equals 90. After that, you will be left with two other acute angles. Choose any one and you can use it as the reference angle A. After that, you will get a long range of ratios for this angle only. You must have heard the term ‘sine’ in Trigonometry. If you want to find how much Sin A is, just divide the perpendicular side with the longest one. The ratio that you will get for that angle will always be constant. Similarly, you can find other ratios such as tan, cos, cotangent, etc. When you use all six functions you will get an entire table.
There are some angles in Mathematics whose ratios you don’t need to calculate. You can directly learn the values of the various trigonometric functions. The best part about this is that it speeds up the process of calculation. For example, the question may ask you to write down the value of tan 45 degrees. In such situations, you don’t have to draw the triangle with that angle and measure the sides. You can directly put the value 1 and calculate the remaining parts. However, not all angles will fall in this category. Only a few of them such as 0, 30, 45, 60, etc. will fall in this position.
What are Identities in Trigonometry?
These are simple formulas with which you can break down the calculation of angles. Instead of finding out the sin of an entire angle, you can break it into an equation. This may be either A + B or A – B. You can apply this equation in the trigonometric function and learn all the identities.
The chapter on trigonometry can be tricky after a certain stage. Keep your basics clear about chapters such as unit circle from websites like Cuemath.