Practice Problems on Trigonometric Functions

1. Find the value of sin(30 degrees) without using a calculator.

2. Calculate cos(45 degrees) without using a calculator.

3. Determine the exact value of tan(60 degrees) without a calculator.

4. If sin(θ) = 0.6, find the value of θ in degrees, where 0° ≤ θ ≤ 90°.

5. Calculate the value of cos(120 degrees) without a calculator.

6. Find the value of tan(π/4) without using a calculator.

7. Given that cos(θ) = -0.8, find the value of θ in degrees, where 0° ≤ θ ≤ 360°.

Trigonometric Functions

Trigonometric Functions, often simply called trig functions, are mathematical functions that relate the angles of a right triangle to the ratios of the lengths of its sides. These Trigonometric functions are fundamental in mathematics for units like Calculus and Geometry and have wide-ranging applications in science, engineering, and various other fields.

In this article, we will in detail about trigonometric functions, their domain and range, and other related facts.

Table of Content

  • What are Trigonometric Functions?
  • Six Trigonometric Functions
  • Trigonometric Functions Formulas
  • Trigonometric Functions Values
  • Trigonometric Functions in Four(4) Quadrants
  • Graphs of Trigonometric Functions
  • Trigonometric Functions Identities
  • Domain and Range of Trigonometric Functions
  • Derivative of Trigonometric Functions
  • Integration of Trigonometric Functions
  • Inverse Trigonometric Functions

Similar Reads

What are Trigonometric Functions?

Trigonometric functions are the basic functions used in trigonometry and they are used for solving various types of problems in physics, Astronomy, Probability, and other branches of science. There are six basic trigonometric functions used in Trigonometry which are:...

Six Trigonometric Functions

The Six Trigonometric Functions are listed below....

Trigonometric Functions Formulas

Formula for various trigonometric functions is given with the help of a right angle triangle. Suppose we have a right angle triangle ABC right angled at B then the side opposite to the angle A is called the perpendicular and the side opposite to angle B is called the Base of the triangle and the side opposite to the right angle is the hypotenuse(which is also the largest side of the triangle)....

Trigonometric Functions Values

Value of trigonometric functions can easily be given using the trigonometry table. These values of the trigonometric functions are very useful in solving the various trigonometric problems. The required trigonometry table is added below:...

Trigonometric Functions in Four(4) Quadrants

The trigonometric functions are the periodic functions and their value repeat after a certain interval. Also, not all the trigonometric functions are positive in all the quadrants....

Graphs of Trigonometric Functions

Trigonometric functions graphs plots the value of the trigonometric functions for different values of the angle(θ). For some the trigonometric functions are bounded as,...

Trigonometric Functions Identities

There are various identities that are related to the trigonometric function these identities link different trigonometric function with each other and are very useful in solving various trigonometric problems. Various trigonometry identities used by us are,...

Domain and Range of Trigonometric Functions

Trigonometric functions are compared to normal functions so the domain and range of the trigonometric functions are comparable to normal function. Suppose we have a trigonometric function f(x) = sin x, then the domain of the function f(x) is all the values of x that the function f(x) can take, and the domain is all possible outcome of the f(x). The domain and range of all the six trigonometric functions are added below,...

Derivative of Trigonometric Functions

Differentiation of trigonometric function can be easily found and which the slope of that curve for that specific value of the trigonometric functions. The differentiation of all six trigonometric functions are added below:...

Integration of Trigonometric Functions

As integration of any curve gives the area under the curve, the integration of trigonometric function also give the area under the trigonometric function. The integration of various trigonometric functions are added below....

Inverse Trigonometric Functions

Inverse Trigonometric Functions are the inverse of the trigonometric function. Suppose we have a trigonometric function f(x) = sin x, such that sin x = a then f-1 (x) is the inverse of f(x) and is called the inverse trigonometric function and is defined as,...

Examples on Trigonometric Functions

Example 1: Simplify (cosec2θ – 1) tan²θ...

Practice Problems on Trigonometric Functions

1. Find the value of sin(30 degrees) without using a calculator....

Trigonometric Functions-FAQs

What are Trigonometric Functions in Maths?...

Contact Us