How to Learn Trigonometry Fast and Raise Grades


There are various topics in mathematics which give students a hard time. Amongst them is trigonometry. The name itself is a little challenging, and even before starting this topic, students lose their minds. Simply giving up is not the solution to this problem. We really need to know how to learn it fast, ensuring all the concepts are embedded in our minds. Private tutoring Sydney is a good option if your child is facing a hard time.

Step 1: Start with the basics

Often, students face a hard time because they just forget the basic rules of mathematics. If you really want to ace trigonometry, it is crucial to start with quadratic equations and linear equations. These concepts may seem that they are way too elementary for trigonometry, but they create an excellent case for understanding this concept. In addition, learning about the different angles is crucial, such as the right angle, straight angle, and full rotation.

Step 2: Right-angle triangle

It is always a good idea to start with a concept that can easily be retained. The right-angle triangle is the one that has one angle, which is 90 degrees. If this is clear to you, then the following steps will become easy. 

Also, the right angle has three sides, namely opposite, hypotenuse and adjacent.

Not to forget, the hypotenuse is the longest side of a right angle.

The three basic rules of sine, cosine, and tangent function in trigonometry should be clear to you a) Sin Theta is equal to O/H, b) Cos Theta is equal to A/H c) Tan Theta is equal to A/O.

You can keep these concepts through the following way:

a) SOH is greater than equal to Sin (Sine)

b) CAH is greater than equal to Cos (Cosine)

c) TAO is greater than equal to Tan (Tangent)

Step 3: Non-right triangle

It may get a bit challenging, but these are special which do not possess any suitable angle. Hence, the Pythagoras theorem can not be applied in this scenario. Sine, cosine, and tangent functions have the same process.

Here you need to understand two crucial points.

a) Sine rule: This rule considers the ratio of the length of a side to the sin of the angle of the opposite side. It is the same for all three sides.

b) Cosine rule: Let a triangle with side a, b and c, the opposite angle should be considered C.

Step 4: Other functions

We are almost there. As we have made some of the most complex rules, here comes the last one.

Learn the important basic identities:

a) sin2 θ when added to cos2 θ equals 1

b) 1 when added to tan2 θ equals sec2 θ

c) 1 when added to cot2 θ equals cosec2 θ

In conclusion, mathematics can be an exciting and also a challenging subject simultaneously. Some pupils enjoy solving complex problems. However, others are reluctant to even listen to the problem and are mentally prepared to give up. Trigonometry is only problematic if we consider it difficult. Learning the basic rules and having command of the identities and ratios will do the job.