Find the value of sin 750.

By Ritesh|Updated : November 4th, 2022

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

Sine Values Table

Sine DegreesValues
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.

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