# Sin Theta Formula

## Sin Theta Formula

Students must recollect a few details regarding the sin function before moving on to learning the Sin Theta Formula. The Sin Theta Formula, often known as the sin function, is a periodic function in Trigonometry. The ratio of the hypotenuse’s length to the perpendicular’s length in a right-angled triangle is another way to describe the sine function. Sin Theta Formula is a periodic function that has a period of 2π and a domain (−∞, ∞) and range of [−1,1], respectively. To determine the sides of a triangle, students must use the Sin Theta Formula.

A trigonometric function called sin x, where x is the angle under discussion stands for the sine of an angle. The Sin Theta Formula is the proportion between the perpendicular and hypotenuse of a right-angled triangle. In other words, the hypotenuse and its value change as the angle changes, and it is the ratio of the side opposite to the angle under discussion. In the study of Physics, sound and light waves are represented by the Sin Theta Formula.

The fundamental characteristics of the sine graph, including its domain and range, derivative, integral, and power series expansion, will be covered in the reference materials available on the Extramarks website and mobile application. A periodic function, the Sin Theta Formula has a period of two.

### Values of sin θ

The table below displays the values of sin θ for different degrees.

 Sin θ degree value 0 0 30 ½ 45 1√2 60 3√2 90 1 180 0

### Formula of Sin Theta

In a right-angled triangle, the ratio between the hypotenuse and the side across from the angle is called the sine of the angle. With a period of two, the Sin Theta Formula is a crucial periodic function in Trigonometry.  The ratio of the lengths of the right-angled triangle’s hypotenuse and perpendicular is how the Sin Theta Formula is expressed. The Sin Theta Formula for a right-angled triangle is expressed as:

sin x = Opposite Side/Hypotenuse = Perpendicular/Hypotenuse in mathematics.

• Sin (- D) = – sin D
• Sin (90 – R) = cos R
• Sin (180 – B) = sin B
• sin2 M + cos2 M = 1
• A+B =Sin A ×Cos B+Cos A ×Sin B
• A-B =Sin A ×Cos B-Cos A ×Sin B
• Sin 2 θ = 2 sin θ. cos θ
• Sin 3 θ = 3 sin θ – 4 sin3 θ

### Solved Example on Sin x Formula

Example 1: Determine the value of Sin x if Cos x = 3/5.

Solution: Cos = BaseHypotenuse is known.

Comparing the ratio, Base equals 3, and Hypotenuse equals 5.

Currently, students are also familiar with Pythagoras’s Theorem, which states that (Hypoteneous)2 = (Base)2 + (Perpendicular)2

(Perpendicular)2 = (Hypoteneous)2 – (Base)2

(Perpendicular)2= 25 – 9

(Perpendicular)2= 16

(Perpendicular) = 4

Since the length of the side cannot be negative, students are only taking positive signals into account here.

Sin x = 4/5

Therefore, this is the correct answer.

Example 2: The value of Sin x should be determined if Cosec x = 6/7.

Answer: Students are aware that sin x = 1/ cosec x.

With the value mentioned above, sin x equals 16/7.

Thus, sin x = 7/6.

### 1. How can students determine the Sin Theta Formula Period?

To find the period of sine function f(x) = Asin Bx + C, students can use the formula, Period = 2π/|B|. For the sine function f(x) = sin x, we have A = 1, B = 1, and C = 0. Students must integrate this value of B into the formula to find the Sin Theta Formula period. Hence, the period of sin x is given by, Period = 2π/|1| = 2π.

### 2. How does the Sin Theta Formula work?

Sin x = Opposite Side/Hypotenuse = Perpendicular/Hypotenuse is the Sin Theta Formula for a sine function. This Sin Theta Formula aids in calculating the sine function sin x, which may be calculated using either the angle x or the lengths of the triangle’s sides.

### 3. Is Sine continuous?

Since the sine curve has no breaks or gaps, the sine graph may be created without having to raise a pen. Additionally, because the Sin Theta Formula is defined for all real values, the graph may be displayed continuously without any breaks. Students can infer that the Sin Theta Formula is continuous as a result.