What is the Easiest Way to Learn Trigonometry?

Trigonometry is a branch of Mathematics that deals with the study of triangles. It is all about the relation between the sides and angles of the triangles. As far as the JEE exam is concerned, trigonometry is an important topic. In this article, we will discuss the easiest way to learn trigonometry.

7 Easy Steps to Learn Trigonometry

Step 1. Study all the basics of trigonometric angles.

Step 2. Study right-angle triangle concepts.

It is a triangle with one angle of 90 degrees. The longest side is the hypotenuse. The other two sides are the adjacent side and the opposite side. The following are the three basic functions in trigonometry.

sine = (opposite side) / hypotenuse

cosine = (adjacent side) / hypotenuse

tangent = (opposite side) / (adjacent side)

Step 3. Pythagoras theorem.

Hypotenuse² = Base² + Altitude²

Step 4.  Sine rule and Cosine rule.

Sine rule: a/ sin A = b/ sin B = c/ sin C

Cosine rule: c² = a² + b² – 2ab cos C

Step 5. List all the important identities of trigonometry.

Fundamental identities:

sin²θ + cos²θ = 1

1 + tan²θ = sec²θ

1 + cot²θ = cosec² θ

Reciprocal formulas:

1/sin x = cosec x

1/cos x = sec x

1/tan x = cot x

Step 6. Remember the trigonometry table.

The table contains the values of trigonometric ratios (sine, cosine, tangent, cotangent, secant, and cosecant) of standard angles.

The following table gives trigonometric ratios for 180°, 270°, and 360°.

Step 7. Be thorough with the trigonometric formulas. Even if you forget the table, you can easily calculate the values using the formulas.

sin x = cos (90°-x)

cos x = sin (90°-x)

tan x = cot (90°-x)

cot x = tan (90°-x)

sec x = cosec (90°-x)

cosec x = sec (90°-x)

Trigonometry becomes easy only when the students are thorough with all the rules and formulas. So, students are recommended to learn all those and practise previous year question papers. This will help them to improve their problem-solving speed and increase their confidence.

Shortcuts and Tricks to Solve JEE Trigonometry Questions

Solved Examples

Example 1: If the angles of a triangle be in the ratio 1 : 2 : 7, then what is the ratio of its greatest side to the least side?

Solution:

x + 2x + 7x = 180^o

⇒ 10x = 180

⇒ x = 180/10 = 18^o

Hence the angles are 18^o, 36^o, 126^o

Greatest side = sin (126^o)

Smallest side = sin (18^o) and

Ratio = sin 126^o / sin (18^o) = [√5 + 1] / [√ 5 − 1]

Example 2: If sinθ + cosθ = 1 then what is the general value of θ?

Solution:

sinθ + cosθ = 1 ⇒ (1 / √2) sinθ + (1 / √2) cosθ = 1 / √2

dividing by √[1² + 1²] = √2,

we get sin (θ + π/4) = [1/ √2] = sin π/4

⇒ θ + π/4 = nπ + (−1)ⁿ [π/4]

⇒ θ = nπ + (−1)ⁿ [π/4] − π/4

Related Articles:

• Trigonometric Equations and its Solutions
• Trigonometric Ratios of Compound Angles

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