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
- If \(4 cos\ θ + 5 sin\ θ = 1\), then all possible values of \(tan\ θ\), is/are
Where, \(θ∈(-\frac \pi2,\frac \pi2)\)- JEE Main - 2024
- Mathematics
- Some Applications of Trigonometry
Height of tower AB is 30 m where B is foot of tower. Angle of elevation from a point C on level ground to top of tower is 60° and angle of elevation of A from a point D x m above C is 15° then find the area of quadrilateral ABCD.
- JEE Main - 2023
- Mathematics
- Some Applications of Trigonometry
Let \(\alpha\ and\ \beta\) be real numbers such that \(-\frac{\pi}{4}<\beta<0<\alpha<\frac{\pi}{4}\). If \(\sin (\alpha+\beta)=\frac{1}{3}\ and\ \cos (\alpha-\beta)=\frac{2}{3}\), then the greatest integer less than or equal to
\(\left(\frac{\sin \alpha}{\cos \beta}+\frac{\cos \beta}{\sin \alpha}+\frac{\cos \alpha}{\sin \beta}+\frac{\sin \beta}{\cos \alpha}\right)^2\) is ____- JEE Advanced - 2023
- Mathematics
- Some Applications of Trigonometry
- A horizontal park is in the shape of a triangle OAB with AB = 16. A vertical lamp post OP is erected at the point O such that\( \begin{array}{l}\angle PAO = \angle PBO = 15^\circ ~\text{and}~ \angle PCO = 45^\circ,\end{array}\)where C is the midpoint of AB. Then (OP)2 is equal to
- JEE Main - 2022
- Mathematics
- Some Applications of Trigonometry
- Consider the following lists:
List I
List II
I $\left\{x \in\left[-\frac{2 \pi}{3}, \frac{2 \pi}{3}\right]: \cos x+\sin x=1\right\}$ P has two elements II $\left\{x \in\left[-\frac{5 \pi}{18}, \frac{5 \pi}{18}\right]: \sqrt{3} \tan 3 x=1\right\} $ Q has three elements III $ \left\{x \in\left[-\frac{6 \pi}{5}, \frac{6 \pi}{5}\right]: 2 \cos (2 x)=\sqrt{3}\right\} $ R has four elements IV $ \left\{x \in\left[-\frac{7 \pi}{4}, \frac{7 \pi}{4}\right]: \sin x-\cos x=1\right\}$ S has five elements T has six elements
The correct option is:- JEE Advanced - 2022
- Mathematics
- Some Applications of Trigonometry
Questions Asked in JEE Main exam
The portion of the line \( 4x + 5y = 20 \) in the first quadrant is trisected by the lines \( L_1 \) and \( L_2 \) passing through the origin. The tangent of an angle between the lines \( L_1 \) and \( L_2 \) is:
- JEE Main - 2024
- Tangents and Normals
- Let \[ \vec{a} = 2\hat{i} + \alpha \hat{j} + \hat{k}, \quad \vec{b} = -\hat{i} + \hat{k}, \quad \vec{c} = \beta \hat{j} - \hat{k}, \] where \( \alpha \) and \( \beta \) are integers and \( \alpha \beta = -6 \). Let the values of the ordered pair \( (\alpha, \beta) \) for which the area of the parallelogram of diagonals \( \vec{a} + \vec{b} \) and \( \vec{b} + \vec{c} \) is \( \frac{\sqrt{21}}{2} \), be \( (\alpha_1, \beta_1) \) and \( (\alpha_2, \beta_2) \). Then \( \alpha_1^2 + \beta_1^2 - \alpha_2 \beta_2 \) is equal to:
- JEE Main - 2024
- Vectors
- The molecular formula of second homologue in the homologous series of monocarboxylic acid is
- JEE Main - 2024
- Aldehydes, Ketones and Carboxylic Acids
- Given below are two statements: Statement I: $\text{PF}_5$ and $\text{BrF}_5$ both exhibit $\text{sp}^3\text{d}$ hybridisation.Statement II: Both $\text{SF}_6$ and $[\text{Co}(\text{NH}_3)_6]^{3+}$ exhibit $\text{sp}^3\text{d}^2$ hybridisation. In the light of the above statements,choose the correct answer from the options given below:
- JEE Main - 2024
- Hybridisation
- Consider the system of linear equations \( x + y + z = 4\mu \), \( x + 2y + 2\lambda z = 10\mu \), \( x + 3y + 4\lambda^2 z = \mu^2 + 15 \), where \( \lambda, \mu \in \mathbb{R} \). Which one of the following statements is NOT correct?
- JEE Main - 2024
- Linear Algebra
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.