Examples on Domain and Range of Trigonometric Functions
Example 1: Find the domain and range of y = sin(x) for all real numbers.
Solution:
The domain and range of y will be as follows:
Domain: R
Range: [−1,1]
Example 2: Determine the domain and range of y = 2cos(3x) for all real values of x.
Solution:
The domain and range of y will be as follows:
Domain: R
Range: [−2,2]
Example 3: Determine the value of y = cot(2x) for x = 8π
Solution:
The value of y at x= 8π
= cot(2× 8π)
= 1
Example 4: Find the domain and range of y = −2tan(x)+1 for all real values of x.
Solution:
The domain and range of y will be as follows:
Domain: R
Range: (−∞, 1)
Example 5: Determine the value of y = cos( 2x) for x= 2π
Solution:
The value of y at x= 2π
= cos(4π)
= 2
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Domain and Range of Trigonometric Functions
Domain and Range of Trigonometric Functions are the values in which the trigonometric function is defined and the output for the domain respectively. Trigonometric Ratios describe relationships between angles and the sides- of right triangles. A Function defined in terms of Trigonometric Ratios is called a Trigonometric Function.
There are a total of six Trigonometric Functions. They play a significant role in various branches of mathematics and science, particularly in calculus and geometry. Trigonometric functions are essential in mathematics and have widespread applications in various fields.
In this article, we will discuss trigonometric functions in detail and learn more about the domain and range of various trigonometric functions.
Table of Content
- What are Trigonometric Functions?
- What is Domain and Range?
- What are the Domain and Range of Trigonometric Functions?
- Domain and Range of Sine Function {Sin(θ)}
- Domain and Range of Cosine Function {Cos (θ)}
- Domain and Range of Tangent Function {Tan (θ)}
- Domain and Range of Cotagent Function {Cot (θ)}
- Domain and Range of Secant Function {Sec (θ)}
- Domain and Range of Cosecant Function {Cosec (θ)}
- Domain and Range of Trig Functions Table
- Domain and Range of Inverse Trigonometric Functions
- Domain and Range of Inverse Trig Functions Table
- Domain and Range of Trig Functions Using Graph
- Examples on Domain and Range of Trigonometric Functions
- Practice Problems on Domain and Range of Trigonometric Functions