Learning Trigonometric Identities Sum

Trigonometry is one of the most important and oldest topics in modern mathematics. The collection of formulas in the trigonometry is usually called as trigonometric function and identities. The trigonometric function and identities are developed to help in the measurement of triangles and their angles. These trigonometric functions and identities are basic tools for understanding many conceptual spaces. Online learning is one of the comfortable method of learning from anywhere around the globe. Through online study, students can learn about trigonometric identities sum. In this topic, we are going to see about, learning trigonometrical identities sum.


The list of trigonometric identities sum are shown below,



Sum or difference of two angles:

sin (a ± b ) = sin a cos b ± cos a sin b

cos(a ± b) = cos a cos b ± sin a sin b

tan(a ± b) = `(tan a +- tan b)/ (1 +- tan a tan b)`



Sum and product formulas:

sin a + sin b = `2sin((a+b)/2)cos((a-b)/2)`

sin a - sin b = `2cos((a+b)/2) sin((a-b)/2)`

cos a + cos b = `2cos((a+b)/2) cos((a-b)/2)`

cos a – cos b = `-2sin((a+b)/2) sin((a-b)/2)`

Learning trigonometrical identities sum: - Examples

Trigonometrical identities sum example 1:

Evaluate Sin 46

Solution:

Sin 46 = Sin (46+1)

= sin 45 cos 1 + cos 45 sin 1

= 0.719(0.999) + 0.707(0.017)

= 0.718 + 0.012

= 0.73

The answer is 0.73



Trigonometrical identities sum example 2:

Evaluate Cos 128

Solution:

Cos 128 = Cos (90 + 38)

= cos 90 cos 38 – sin 90 sin 38

= 0(0.788) – 1(0.615)

= 0 – 0.615

= -0.615

The answer is -0.615



Trigonometrical identities sum example 3:

Evaluate tan 50

Solution:

Tan 50 = Tan (45 + 5)

= `(tan 45 + tan 5)/(1-tan 45*tan 5)`

= `(1+0.087)/(1-(1*0.087))`

= `1.087/(1-0.087)`

= `1.087/ 0.913`

= 1.190

The answer is 1.190


Trigonometrical identities sum example 4

Evaluate Cos 92

Solution:

Cos 92 = cos (90+2)

= cos 90 cos 2 - sin 90 sin 2

= 0(0.999) - 1(0.034)

= 0 + 0.034

= 0.034

The answer is 0.034