Value of Sin 15

# Value of Sin 15

## Introduction to Value of sin 15

The sine of 15 degrees, abbreviated sin 15°, is a trigonometric function that expresses the ratio of the length of a right triangle’s side opposite a 15-degree angle to the length of the hypotenuse. It is an irrational number that is roughly equivalent to 0.2588.

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### The Value of Sin 15°

To get the value of Sin 15°, consider the formula for compound angles.

Sin(A – B) = sinA cosB – cosA sinB

Substitute the values A = 45°, B = 30°

### The Value of Sin 15° in decimal value:

The value Sin 15° of in the decimal values:

We know that

Therefore, the decimal value of Sin 15° is 0.2588

### The value of cos 15

To get the value of Cos 15° degrees, consider the formula for compound angles.

Cos(A – B) = cosA cosB – sinA sinB

Substitute the values A = 45°, B = 30°

### Problems involving sin 15

Problem No. 1: Find the value of sin 15° + sin 30° .cos 15°

Solution: The given expression is sin 15° + sin 30° .cos 15°

Plug in the values

Problem No. 2: Find the value of Sin 15° – Cos 15°

Solution: The given expression is Sin 15° – Cos 15°

## Frequently asked questions about sin 15 degrees

### What is the value of the sin 15?

opposite to the angle to the length of the hypotenuse in a right triangle. To find the sine of 15 degrees, we can draw a right triangle with one of the angles as 15 degrees. Using basic trigonometric ratios, sine theta = opposite side/hypotenuse. For a 15 degree angle, the opposite side will be 0.2588 and hypotenuse will be 1. So, sin 15 = 0.2588.

### What is the value of 15 in trigonometry?

15 degrees represents an acute angle measuring one-twenty-fourth of a full circle rotation. One full rotation is 360 degrees, so 15 degrees would be 360/24 = 15 degrees. 15 degrees is a common angle used in trigonometry problems involving 30-60-90 degree special right triangles. Knowing the trig values of 15 degrees is useful for solving many problems.

### What is value of cos 15?

cosine of an angle is the ratio of the length of the side adjacent to the angle to the length of the hypotenuse. Using a 15 degree right triangle with hypotenuse 1 and opposite side 0.2588, we can determine the adjacent side using Pythagorean theorem. Adjacent side = sqrt(1^2 - 0.2588^2) = 0.9659. Therefore, cos 15 = adjacent/hypotenuse = 0.9659.

### How do you find sin 15 without a calculator?

sin 15 without calculator, you can construct a 30-60-90 degree special right triangle, which contains an angle of 30 degrees and another of 60 degrees. The hypotenuse is always twice the length of the shorter side. For a hypotenuse of 2, the shorter side is 1. Sin 30 = Opposite/Hypotenuse = 1/2 = 0.5. Sin 15 is half of sin 30, so sin 15 = 0.5/2 = 0.2588.

### What is cos 15 degrees in terms of sine?

We know that the sine, cosine and tangent of an angle have certain relationships. Since sum of angles of a triangle is 180 degrees, cos 15 = sin (180 - 15) = sin 165. 165 can be simplified to 75 (360 - 165). Therefore, cos 15 degrees = sin 75 degrees.

### What is the value of sin 18?

sin 18, we can use a calculator which gives 0.3090. Or construct a 36-54-90 triangle with hypotenuse 2. Here, shorter side = 1, so sin 36 = Opposite/Hypotenuse = 1/2 = 0.5. Sin 18 is half of sin 36, so sin 18 = 0.5/2 = 0.3090.

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