How to solve basic problems in trigonometry?(concept-2)

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IB Mathematics Tutor give great importance to Trigonometry

Trigonometry is one of the fascinating branches of Mathematics. It deals with the relationships between the sides and angles of a triangle. Word trigonometry was originated from the Greek word, where, ‘TRI‘ means Three‘GON‘ means sides and the ‘METRON’ means to measure. It’s an ancient and probably the most widely used branch of Mathematics.

For basic learning, Mathematics tutor divide trigonometry in two-part:-

1 Trigonometry based on right triangles

1 Trigonometry based on non-right triangles.

In this post, we will discuss problems based on trigonometric ratios of a few specific angles like 0°,30°, 45°, 60° and 90°. Mathematics tutor use different tricks to form this table. I will discuss my tricks in a separate post

Concept-2

In a trigonometric problem, If we are given a trigonometric ratio with a specific angle, we will first put the value of that ratio from the above table and do simplification. Simplification is usually based on L.C.M and rationalization.

Also READ this-  How to solve basic problems in trigonometry?(concept-1)

Example-1 Find the value of 4/3 tan²60° + 3 cos²30° – 2 sec²30° – 3/4 cot²60°

Solution:  4/3 tan²60° + 3 cos²30° – 2 sec²30° – 3/4 cot²60°

=4/3(√3)²+3(√3/2)²-2(2/√3)²-3/4(1/√3)²
=4/3(3)+3(3/4)-2(4/3)-3/4(1/3)
=4+9/4-8/3-1/3
=4+9/4-3
=16+9-12/3
=13/3

Example-2 If A = 60° and B = 30°, verify sin (A – B) = sin A cos B – cos A sin B

Solution:

L.H.S. = sin (A – B)

= sin (60° – 30°)

= sin 30°

= ½

R.H.S. = sin A cos B – cos A sin B

= sin 60° cos 30° – cos 60° sin 30°

32×3212×12

= ¾ – ¼

= 2/4

= ½

Therefore, L.H.S. = R.H.S. (Proved)

To get a better understanding of the concept you should check all my posts of Mathematics tutor series. you can check them by clicking on the links given below

First post- concept one

Second post- concept two(current post)

Third post -Concept three

Fourth post -Concept four

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    2 comments

    1. My name is Ravi K , I am Mathematics Lecturer I want to join your group as a tutor. What are the step should one follow to join the group as a tutor?, please let me know.
      Thank you,
      Ravi K

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