Introduction to trigonometric identities sum help:
Trigonometry is arrived from the Greek word, trigonon = triangle and metron = measure. The father of trigonometry is Hipparchus. He designed the first trigonometric table. Trigonometry has wide range of applications in many fields like science, technology, astronomy etc. Identity is defined as an equation that is true for all probable values of its variables. Online help is one of the comfortable method of getting help from anywhere around the globe. Through online study, students can get about trigonometric identities sum. In this topic, we are going to see about, trigonometric identities sum help. I like to share this Pythagorean Trigonometric Identities with you all through my article.
Trigonometric Identities Sum Help - Trigonometric Identities:
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)`
Is this topic the Pythagorean theorem hard for you? Watch out for my coming posts.
Trigonometric Identities Sum Help: - Examples
Example 1:
Evaluate Sin 153
Solution:
Sin 153 = Sin (90+63)
= sin 90 cos 63 + cos 90 sin 63
= 1(0.454) + 0(0.891)
= 0.454 + 0
= 0.454
The answer is 0.454
Example 2:
Evaluate Cos 128
Solution:
Cos 128 = Cos (90 + 38)
= cos 90 cos 38 – sin 90 sin 38
= 0(0.788) – 1(0.616)
= 0 – 0.616
= -0.616
The answer is -0.616
Example 3:
Evaluate tan 38
Solution:
Tan 38 = Tan (45 - 7)
= `(tan 45 - tan 7)/(1+tan 45*tan 7)`
= `(1-0.123)/(1+(1*0.123))`
= `0.877/(1+0.123)`
=` 0.877/ 1.123`
= 0.781
The answer is 0.781
Example 4
Evaluate Cos 124
Solution:
Cos 124 = cos (90 + 34)
= cos 90 cos 34 - sin 90 sin 34
= 0(0.829) - 1(0.559)
= 0 – 0-0.559
= -0.559
The answer is -0.559
Example 5:
Evaluate, sin 50 - sin 40
Solution:
sin a - sin b = `2cos((a+b)/2)sin((a-b)/2)`
sin 50 - sin 40 = `2 cos((50+40)/2)sin((50-40)/2)`
= `2 cos (90/2) sin(10)/2`
= 2 cos 45 sin 5
= 2 (0.707)(0.087)
= 2 * 0.062
= 0.124
The answer is 0.124
Trigonometry is arrived from the Greek word, trigonon = triangle and metron = measure. The father of trigonometry is Hipparchus. He designed the first trigonometric table. Trigonometry has wide range of applications in many fields like science, technology, astronomy etc. Identity is defined as an equation that is true for all probable values of its variables. Online help is one of the comfortable method of getting help from anywhere around the globe. Through online study, students can get about trigonometric identities sum. In this topic, we are going to see about, trigonometric identities sum help. I like to share this Pythagorean Trigonometric Identities with you all through my article.
Trigonometric Identities Sum Help - Trigonometric Identities:
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)`
Is this topic the Pythagorean theorem hard for you? Watch out for my coming posts.
Trigonometric Identities Sum Help: - Examples
Example 1:
Evaluate Sin 153
Solution:
Sin 153 = Sin (90+63)
= sin 90 cos 63 + cos 90 sin 63
= 1(0.454) + 0(0.891)
= 0.454 + 0
= 0.454
The answer is 0.454
Example 2:
Evaluate Cos 128
Solution:
Cos 128 = Cos (90 + 38)
= cos 90 cos 38 – sin 90 sin 38
= 0(0.788) – 1(0.616)
= 0 – 0.616
= -0.616
The answer is -0.616
Example 3:
Evaluate tan 38
Solution:
Tan 38 = Tan (45 - 7)
= `(tan 45 - tan 7)/(1+tan 45*tan 7)`
= `(1-0.123)/(1+(1*0.123))`
= `0.877/(1+0.123)`
=` 0.877/ 1.123`
= 0.781
The answer is 0.781
Example 4
Evaluate Cos 124
Solution:
Cos 124 = cos (90 + 34)
= cos 90 cos 34 - sin 90 sin 34
= 0(0.829) - 1(0.559)
= 0 – 0-0.559
= -0.559
The answer is -0.559
Example 5:
Evaluate, sin 50 - sin 40
Solution:
sin a - sin b = `2cos((a+b)/2)sin((a-b)/2)`
sin 50 - sin 40 = `2 cos((50+40)/2)sin((50-40)/2)`
= `2 cos (90/2) sin(10)/2`
= 2 cos 45 sin 5
= 2 (0.707)(0.087)
= 2 * 0.062
= 0.124
The answer is 0.124
