
CBSE Important Questions›

CBSE Previous Year Question Papers›
 CBSE Previous Year Question Papers
 CBSE Previous Year Question Papers Class 12
 CBSE Previous Year Question Papers Class 10

CBSE Revision Notes›

CBSE Syllabus›

CBSE Extra Questions›

CBSE Sample Papers›
 CBSE Sample Papers
 CBSE Sample Question Papers For Class 5
 CBSE Sample Question Papers For Class 4
 CBSE Sample Question Papers For Class 3
 CBSE Sample Question Papers For Class 2
 CBSE Sample Question Papers For Class 1
 CBSE Sample Question Papers For Class 12
 CBSE Sample Question Papers For Class 11
 CBSE Sample Question Papers For Class 10
 CBSE Sample Question Papers For Class 9
 CBSE Sample Question Papers For Class 8
 CBSE Sample Question Papers For Class 7
 CBSE Sample Question Papers For Class 6

ISC & ICSE Syllabus›

ICSE Question Paper›
 ICSE Question Paper
 ISC Class 12 Question Paper
 ICSE Class 10 Question Paper

ICSE Sample Question Papers›
 ICSE Sample Question Papers
 ISC Sample Question Papers For Class 12
 ISC Sample Question Papers For Class 11
 ICSE Sample Question Papers For Class 10
 ICSE Sample Question Papers For Class 9
 ICSE Sample Question Papers For Class 8
 ICSE Sample Question Papers For Class 7
 ICSE Sample Question Papers For Class 6

ICSE Revision Notes›
 ICSE Revision Notes
 ICSE Class 9 Revision Notes
 ICSE Class 10 Revision Notes

ICSE Important Questions›

Maharashtra board›

RajasthanBoard›
 RajasthanBoard

Andhrapradesh Board›
 Andhrapradesh Board
 AP Board Sample Question Paper
 AP Board syllabus
 AP Board Previous Year Question Paper

Telangana Board›

Tamilnadu Board›

NCERT Solutions Class 12›
 NCERT Solutions Class 12
 NCERT Solutions Class 12 Economics
 NCERT Solutions Class 12 English
 NCERT Solutions Class 12 Hindi
 NCERT Solutions Class 12 Maths
 NCERT Solutions Class 12 Physics
 NCERT Solutions Class 12 Accountancy
 NCERT Solutions Class 12 Biology
 NCERT Solutions Class 12 Chemistry
 NCERT Solutions Class 12 Commerce

NCERT Solutions Class 10›

NCERT Solutions Class 11›
 NCERT Solutions Class 11
 NCERT Solutions Class 11 Statistics
 NCERT Solutions Class 11 Accountancy
 NCERT Solutions Class 11 Biology
 NCERT Solutions Class 11 Chemistry
 NCERT Solutions Class 11 Commerce
 NCERT Solutions Class 11 English
 NCERT Solutions Class 11 Hindi
 NCERT Solutions Class 11 Maths
 NCERT Solutions Class 11 Physics

NCERT Solutions Class 9›

NCERT Solutions Class 8›

NCERT Solutions Class 7›

NCERT Solutions Class 6›

NCERT Solutions Class 5›
 NCERT Solutions Class 5
 NCERT Solutions Class 5 EVS
 NCERT Solutions Class 5 English
 NCERT Solutions Class 5 Maths

NCERT Solutions Class 4›

NCERT Solutions Class 3›

NCERT Solutions Class 2›
 NCERT Solutions Class 2
 NCERT Solutions Class 2 Hindi
 NCERT Solutions Class 2 Maths
 NCERT Solutions Class 2 English

NCERT Solutions Class 1›
 NCERT Solutions Class 1
 NCERT Solutions Class 1 English
 NCERT Solutions Class 1 Hindi
 NCERT Solutions Class 1 Maths

JEE Main Question Papers›

JEE Main Syllabus›
 JEE Main Syllabus
 JEE Main Chemistry Syllabus
 JEE Main Maths Syllabus
 JEE Main Physics Syllabus

JEE Main Questions›
 JEE Main Questions
 JEE Main Maths Questions
 JEE Main Physics Questions
 JEE Main Chemistry Questions

JEE Main Mock Test›
 JEE Main Mock Test

JEE Main Revision Notes›
 JEE Main Revision Notes

JEE Main Sample Papers›
 JEE Main Sample Papers

JEE Advanced Question Papers›

JEE Advanced Syllabus›
 JEE Advanced Syllabus

JEE Advanced Mock Test›
 JEE Advanced Mock Test

JEE Advanced Questions›
 JEE Advanced Questions
 JEE Advanced Chemistry Questions
 JEE Advanced Maths Questions
 JEE Advanced Physics Questions

JEE Advanced Sample Papers›
 JEE Advanced Sample Papers

NEET Eligibility Criteria›
 NEET Eligibility Criteria

NEET Question Papers›

NEET Sample Papers›
 NEET Sample Papers

NEET Syllabus›

NEET Mock Test›
 NEET Mock Test

NCERT Books Class 9›
 NCERT Books Class 9

NCERT Books Class 8›
 NCERT Books Class 8

NCERT Books Class 7›
 NCERT Books Class 7

NCERT Books Class 6›
 NCERT Books Class 6

NCERT Books Class 5›
 NCERT Books Class 5

NCERT Books Class 4›
 NCERT Books Class 4

NCERT Books Class 3›
 NCERT Books Class 3

NCERT Books Class 2›
 NCERT Books Class 2

NCERT Books Class 1›
 NCERT Books Class 1

NCERT Books Class 12›
 NCERT Books Class 12

NCERT Books Class 11›
 NCERT Books Class 11

NCERT Books Class 10›
 NCERT Books Class 10

Chemistry Full Forms›
 Chemistry Full Forms

Biology Full Forms›
 Biology Full Forms

Physics Full Forms›
 Physics Full Forms

Educational Full Form›
 Educational Full Form

Examination Full Forms›
 Examination Full Forms

Algebra Formulas›
 Algebra Formulas

Chemistry Formulas›
 Chemistry Formulas

Geometry Formulas›
 Geometry Formulas

Math Formulas›
 Math Formulas

Physics Formulas›
 Physics Formulas

Trigonometry Formulas›
 Trigonometry Formulas

CUET Admit Card›
 CUET Admit Card

CUET Application Form›
 CUET Application Form

CUET Counselling›
 CUET Counselling

CUET Cutoff›
 CUET Cutoff

CUET Previous Year Question Papers›
 CUET Previous Year Question Papers

CUET Results›
 CUET Results

CUET Sample Papers›
 CUET Sample Papers

CUET Syllabus›
 CUET Syllabus

CUET Eligibility Criteria›
 CUET Eligibility Criteria

CUET Exam Centers›
 CUET Exam Centers

CUET Exam Dates›
 CUET Exam Dates

CUET Exam Pattern›
 CUET Exam Pattern
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 rightangled 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 rightangled 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.
History of Trigonometry
In a rightangled 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. Students should think about a unit circle with its centre at the origin of the coordinate plane to better grasp how sin x is derived. On the perimeter (border) of this circle, a variable point P moves. They must pay attention to the fact that P is in the first quadrant and that OP forms an acute angle of x radians with the positive xaxis. The angle PQ is perpendicular to the horizontal axis dropped from P. As seen in the diagram provided on the Extramarks website and mobile application, the triangle is created by connecting the points O, P, and Q.
Trigonon and metron, two Greek words that signify triangle and measure respectively, are the source of the word Trigonometry. However, up to the 16th century, when the other values of the components were recorded, the major focus was on numerically determining the values of the missing triangle parts. In order to further illustrate the notion, students must start with an example while keeping this in mind. If just the length of the triangle’s two sides and the measurement of the contained angle are provided, the third and remaining two angles may be determined. Trigonometry differs from Geometry in that it examines qualitative relationships. Nevertheless, Trigonometry was regarded as a component of Geometry until the 16th century, when it was separated into its own branch of Mathematics.
Trigonometry originated with the Greeks in the modern sense, and Hipparchus was the first to compile a table of the values of the trigonometric function. These concepts were described geometrically at the time, such as relationships between the angles that subtended them and the chords of different shapes. Additionally, the present symbols for trigonometric functions were not created until the 17th century.
However, due to two Frenchinspired advancements, Trigonometry began to transition from a geometric discipline to an algebraicanalytic science throughout the 16th century. It was the development of Analytical Geometry and the birth of symbolic Algebra.
Origin of the Trigonometry
Aryabhatta used the concept of “Sin Theta Formula” in his work for the first time around 500 A.D. He adopted the term “ardhajya,” which in due time was abbreviated to “jive” or “jya.” However, when the Arabic term jiva was translated, it became the Latin word sinus, which denoted curvature. After then, the term sinus was replaced by Sin Theta Formula in future mathematical terminology across Europe. Additionally, Edmund Gunter, an English professor of astronomy, coined the term “Sin Theta Formula” for the first shortened notation.
Trigonometric Ratios
There are about six trigonometric ratios – sine, cosine, tangent, cosecant, secant, and cotangent – which describe the many configurations that may be made in a rightangled triangle.
Trigonometry can only be used to solve a side of a rightangled triangle when the lengths of the other two sides and the angle of a side are already known. Before utilising Algebra to get the value for the unknown side, one must first select a ratio that includes both the unknown and the provided sides.
Sin Theta Formula
The ratio of the lengths of the rightangled triangle’s hypotenuse and perpendicular is how the Sin Theta Formula is expressed. The Sin Theta Formula for a rightangled triangle is expressed as:
sin x = Opposite Side/Hypotenuse = Perpendicular/Hypotenuse in mathematics.
Example on Sin x Formula
 Determine the value of Sin x if Cos x = 35.
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 Hypotenuse2 = Base2 + Perpendicular2
(Perpendicular)2= (Hypotenuse) (Hypotenuse)
(Perpendicular)2 = 25 – 9
(Perpendicular)2 = 16
(Perpendicular)2 = 42 (Base)2
(Perpendicular)2 = 52 – 32
Since the length of the side cannot be negative, students are only taking positive signals into account here.
Sin x – 45
Therefore, this is the correct answer.
 The value of Sin x should be determined if Cosec x = 67.
Answer: Students are aware that sin x = 1cosec x.
With the value mentioned above, sin x equals 16/7.
Thus, sin x = 76.
Brief Overview of Trigonometry
The area of Mathematics known as Trigonometry studies the relationship between angles and the length—not the arc length—of a line formed by an angle. Anytime one discusses angles, there must be two crossing lines through which the angle was formed. One also requires an additional line on which to measure the length. In summary, one requires three lines. The acronym “tri” stands for that. Students must now be aware of several triangle kinds. The triangle should thus have a right angle.
FAQs (Frequently Asked Questions)
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.