In this article, we will discuss some important formula and short notes and basics of trigonometry ratio and identity to solve trigonometry questions of quickly during the NDA exam.
Trigonometry is very simple if you study it very well and in a systematic manner and clear of concept of trigonometry it helps in during the NDA exam . Let us understand the basics of trigonometry one by one as described below-
I . Trigonometric Ratios –
The six trigonometric ratios are sine (sin), cosine (cos), tangent (tan), cotangent (cot), cosecant (cosec), and secant (sec). In geometry trigonometry is a branch of mathematics that deals with the sides and angles of a right-angled triangle. Therefore, trig ratios are evaluated with respect to sides and angles.
The trigonometry ratios for a specific angle ‘’ is given below:
Trigonometry ratio table:
The trigonometric ratios for some specific angles such as 0 °, 30 °, 45 °, 60 ° and 90° are given below, which are commonly used in mathematical calculations.
From this table, we can find the value for the trigonometric ratios for these angles
Trigonometric Ratios Identities:
There are many trigonometric ratios identities that we use to make our calculations easier and simpler. These include identities of complementary angles, supplementary angles, Pythagorean identities, and sum, difference, product identities.
Trigonometric Ratios of Complementary Angles
The complementary angles are a pair of two angles such that their sum is equal to 90°. The complement of an angle is. The trigonometric ratios of complementary angles are:
Trigonometric Ratios of Supplementary Angles
The supplementary angles are a pair of two angles such that their sum is equal to 180°. The supplement of an angle is. The trigonometric ratios of supplementary angles are:
Pythagorean Trigonometric Ratios Identities
The Pythagorean trigonometric ratios identities in trigonometry are derived from the Pythagoras thermo Applying Pythagoras theorem to the right-angled triangle below, we get:
Dividing both sides by
we can derive two other Pythagorean trigonometric ratios identities:
Sum, Difference, Product Trigonometric Ratios Identities
The sum, difference, and product trigonometric ratios identities include the formulas of sin(A+B), sin(A-B), cos(A+B), cos(A-B), etc.
Half, Double, and Triple-Angles Trigonometric Ratios Identities
Double Angle Trigonometric Ratios Identities
The double angle trigonometric identities can be obtained by using the sum and difference formulas.
For example, from the above formula sin (A+B) = sin A cos B + cos A sin B
Substitute A = B = on both sides here, we get:
In the same way, we can derive the other double angle identities.
Half Angle Trigonometric Ratios Identities:
Using one of the above double angle formulas,
Replacing by on both sides,
This is the half-angle formula of sine
In the same way, we can derive the other half-angle formulas.
Triple Angle Trigonometric Ratios Identities