The value of sin75° is
Answers
EXPLANATION.
Value of sin75°.
As we know that,
We can write equation as,
⇒ sin(75°) = sin(45° + 30°).
As we know that,
Formula of :
⇒ sin(A + B) = sin(A).cos(B) + cos(A).sin(B).
Put the values in the equation, we get.
⇒ sin(45° + 30°) = sin(45°).cos(30°) + cos(45°).sin(30°).
⇒ sin(45° + 30°) = 1/√2 x √3/2 + 1/√2 x 1/2.
⇒ sin(45° + 30°) = √3/2√2 + 1/2√2.
⇒ sin(45° + 30°) = (√3 + 1)/2√2.
⇒ sin(75°) = (√3 + 1)/2√2.
MORE INFORMATION.
(1) = sin(A ± B) = sin(A).cos(B) ± cos(A).sin(B).
(2) = cos(A + B) = cos(A).cos(B) - sin(A).sin(B).
(3) = cos(A - B) = cos(A).cos(B) + sin(A).sin(B).
(4) = tan(A + B) = tan(A) + tan(B)/1 - tan(A).tan(B).
(5) = tan(A - B) = tan(A) - tan(B)/1 + tan(A).tan(B).
❀Answer: (√3 + 1)/ 2√2
☆EXPLANATION☆
Sin 75 we can write it as
Sin 75 = Sin(45+30)…………………..(1)
By applying the formula
Sin (A + B) = Sin A. Cos B + Cos A. Sin B
Sin (45 + 30) = Sin 45. Cos 30 + Cos 45. Sin 30…………………..(2)
Sin Values
sin 0° = √(0/4) = 0
sin 30° = √(1/4) = ½
sin 45° = √(2/4) = 1/√2
sin 60° = √3/4 = √3/2
cos 90° = √(4/4) = 1
Cos Values
cos 0° = √(4/4) = 1
cos 30° = √(3/4) = √3/2
cos 45° = √(2/4) = 1/√2
cos 60° = √(1/4) = 1/2
cos 90° = √(0/4) = 0
Substitute the value of sin 30, sin 45, cos 30 and cos 45 degrees, then equation (2) will becomes
Sin (45 + 30) = Sin 45. Cos 30 + Cos 45. Sin 30
Sin (45 + 30) = 1/√2 . √3/2 + 1/√2 . 1/2
Sin (45 + 30) = (√3 + 1) / 2√2
Hence the value of Sin 75 degree is equal to (√3 + 1) / 2√2.