If \(4 cos\ θ + 5 sin\ θ = 1\), then all possible values of \(tan\ θ\), is/are
Where, \(θ∈(-\frac \pi2,\frac \pi2)\)
Where, \(θ∈(-\frac \pi2,\frac \pi2)\)
- 1
- 3
- 2
- 4
The Correct Option is C
Solution and Explanation
The correct option is (C): 2.
Top Questions on Some Applications of Trigonometry
- 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}.
- JEE Advanced - 2025
- Mathematics
- Some Applications of Trigonometry
- In \( \triangle ABC \), if \( AB = 6\sqrt{3} \) cm, \( AC = 12 \) cm and \( BC = 6 \) cm, then the angle \( B \) is:
- TS POLYCET - 2025
- Mathematics
- Some Applications of Trigonometry
- If \(\frac {3cos\ 2x+cos^32x}{cos^6x-sin^6x}=x^3-x^2+6\), then find sum of roots.
- JEE Main - 2024
- 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
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
Questions Asked in JEE Main exam
Statement-1: \( \text{ClF}_3 \) has 3 possible structures.
Statement-2: \( \text{III} \) is the most stable structure due to least lone pair-bond pair (lp-bp) repulsion.
Which of the following options is correct?
- JEE Main - 2025
- Molecular Stability
Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason (R).
Assertion (A): Choke coil is simply a coil having a large inductance but a small resistance. Choke coils are used with fluorescent mercury-tube fittings. If household electric power is directly connected to a mercury tube, the tube will be damaged.
Reason (R): By using the choke coil, the voltage across the tube is reduced by a factor \( \frac{R}{\sqrt{R^2 + \omega^2 L^2}} \), where \( \omega \) is the frequency of the supply across resistor \( R \) and inductor \( L \). If the choke coil were not used, the voltage across the resistor would be the same as the applied voltage.
In light of the above statements, choose the most appropriate answer from the options given below:
- JEE Main - 2025
- Electromagnetism
- Let \( (2, 3) \) be the largest open interval in which the function \( f(x) = 2 \log_e (x - 2) - x^2 + ax + 1 \) is strictly increasing, and \( (b, c) \) be the largest open interval, in which the function \( g(x) = (x - 1)^3 (x + 2 - a)^2 \) is strictly decreasing. Then \( 100(a + b - c) \) is equal to:
- JEE Main - 2025
- Quadratic Equations
- If \( \alpha + i\beta \) and \( \gamma + i\delta \) are the roots of the equation \( x^2 - (3-2i)x - (2i-2) = 0 \), \( i = \sqrt{-1} \), then \( \alpha\gamma + \beta\delta \) is equal to:
- JEE Main - 2025
- Complex numbers
- If \( \alpha \) and \( \beta \) are the roots of the equation \( 2z^2 - 3z - 2i = 0 \), where \( i = \sqrt{-1} \), then \[ 16 \cdot {Re} \left( \frac{\alpha^{19} + \beta^{19} + \alpha^{11} + \beta^{11}}{\alpha^{15} + \beta^{15}} \right) \cdot {Im} \left( \frac{\alpha^{19} + \beta^{19} + \alpha^{11} + \beta^{11}}{\alpha^{15} + \beta^{15}} \right) \] is equal to:
- JEE Main - 2025
- Complex numbers
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.