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Find the value of sin 750.
By BYJU'S Exam Prep
Updated on: September 25th, 2023
The value of sin 750 is (√3 + 1)/2√2. The ratio between the side perpendicular to the angle and the hypotenuse is known as the sine of an angle in a right-angled triangle.
Sin α= Opposite side/ Hypotenuse
or
Sin α = Perpendicular/Hypotenuse
Now we have to find the value of the given trigonometric ratio.
Given trigonometric ratio: sin 750
sin 750 is expressed as sin 750 = sin (450 + 300)
We know that the trigonometric formula sin (A + B) = sin A cos B + cos A sin B
Thus, using the aforementioned formula, we obtain
sin 750 = sin 450 cos 300 + cos 450 sin 300
As sin 450 = 1/√2, cos 300 = √3/2, cos 450 = 1/√2 and sin 300 = ½
By substituting the values in above equation we get,
sin 750 = [1/√2 x √3/2] + [1/√2 x ½]
= √3/2√2 + 1/2√2
= (√3 + 1)/2√2
Therefore, the value of sin 750 is (√3 + 1)/2√2
Table of content
Sine Values Table
Sine Degrees | Values |
Sine 0° | 0 |
Sine 30° | 1/2 |
Sine 45° | 1/√2 |
Sine 60° | √3/2 |
Sine 90° | 1 |
Sine 120° | √3/2 |
Sine 150° | 1/2 |
Sine 180° | 0 |
Sine 270° | -1 |
Sine 360° | 0 |
Summary:
Find the value of sin 750.
(√3 + 1)/2√2 is the value of sin 750. In trigonometry, the sine function can be explained as the ratio of the hypotenuse length to the opposite side length of a right-angled triangle. It is used to determine the side length or unknown angles.