If \(\frac {3cos\ 2x+cos^32x}{cos^6x-sin^6x}=x^3-x^2+6\), then find sum of roots.
Correct Answer: 1
Solution and Explanation
Top Questions on Some Applications of Trigonometry
- A ladder 7 m long makes an angle of 30\(^\circ\) with the wall. Find the height of the point on the wall where the ladder touches the wall.
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- The angle of elevation of the top of a tower at a distance of 10 m from its base is 60\(^\circ\); then the height of the tower is
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- A kite is at a height of 30 m from the earth and its string makes an angle 60\(^\circ\) with the earth. Then the length of the string is
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- The shadow of a tower, when the angle of elevation of the sun is $30^\circ$, is $50$ m longer than when the angle of elevation was $60^\circ$ on the plane ground. Find the height of the tower.
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- Let $$ \alpha = \frac{1}{\sin 60^\circ \sin 61^\circ} + \frac{1}{\sin 62^\circ \sin 63^\circ} + \cdots + \frac{1}{\sin 118^\circ \sin 119^\circ}. $$ Then the value of $$ \left( \frac{\csc 1^\circ}{\alpha} \right)^2 $$ is \rule{1cm}{0.15mm}.
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Questions Asked in JEE Main exam
Consider the following sequence of reactions :
Molar mass of the product formed (A) is ______ g mol\(^{-1}\).- JEE Main - 2025
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- A wire of resistance R is bent into an equilateral triangle and an identical wire is bent into a square. The ratio of resistance between the two end points of an edge of the triangle to that of the square is:
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- Three infinitely long wires with linear charge density \( \lambda \) are placed along the x-axis, y-axis and z-axis respectively. Which of the following denotes an equipotential surface?
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Two capacitors \( C_1 \) and \( C_2 \) are connected in parallel to a battery. Charge-time graph is shown below for the two capacitors. The energy stored with them are \( U_1 \) and \( U_2 \), respectively. Which of the given statements is true?
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Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Time period of a simple pendulum is longer at the top of a mountain than that at the base of the mountain.
Reason (R): Time period of a simple pendulum decreases with increasing value of acceleration due to gravity and vice-versa. In the light of the above statements, choose the most appropriate answer from the options given below:- JEE Main - 2025
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Concepts Used:
Some Applications of Trigonometry
Trigonometry is a branch of mathematics that deals with the relationships between the sides and angles of triangles. It has many practical applications in various fields, including science, engineering, architecture, and navigation. Here are some examples:
- Architecture: Trigonometry is used in designing buildings and structures, particularly in determining the height and angles of roofs, the dimensions of rooms, and the placement of windows.
- Engineering: Trigonometry is used in many engineering fields, such as civil, mechanical, and electrical engineering. It is used to calculate the angles, distances, and dimensions of objects in 2D and 3D space, as well as to solve complex problems involving force, motion, and energy.
- Astronomy: Trigonometry is used to calculate the positions and movements of celestial bodies, such as planets and stars.
- Surveying: Trigonometry is used in surveying to measure distances, heights, and angles of land features, as well as to create maps and blueprints.
- Navigation: Trigonometry is used in navigation, both on land and at sea, to determine position, distance, and direction. It is also used in aviation to calculate the trajectory and speed of airplanes.
- Physics: Trigonometry is used in physics to calculate the behavior of waves, such as sound and light waves, and to solve problems involving motion and force.
Read Also: Some Applications of Trigonometry
Overall, trigonometry is a versatile tool that has many practical applications in various fields and continues to be an essential part of modern mathematics.