-
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›
-
Rajasthan-Board›
- Rajasthan-Board
-
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 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.
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.