(C) We know that the range of the cosine function is $-1 \leq \cos \theta \leq 1$. Multiplying throughout by $5$,we get $-5 \leq 5 \cos \theta \leq 5$

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

(C) We know that the range of the cosine function is $-1 \leq \cos \theta \leq 1$. Multiplying throughout by $5$,we get $-5 \leq 5 \cos \theta \leq 5$. Adding $12$ to all parts of the inequality,we get $-5 + 12 \leq 5 \cos \theta + 12 \leq 5 + 12$. This simplifies to $7 \leq 5 \cos \theta + 12 \leq 17$. Thus,the smallest value of the expression $5 \cos \theta + 12$ is $7$.

Class 11 Mathematics Trigonometrical Ratios, Functions and Identities Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

Easy

The smallest value of $5 \cos \theta + 12$ is

WBJEE 2009 All WBJEE

A
$5$
B
$12$
C
$7$
D
$17$

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

Trigonometrical Ratios, Functions and Identities

Subtopic

Maximum and minimum values of trigonometrical functions, Conditional trigonometrical identities

Previous Year

WBJEE 2009 Paper All WBJEE years →

The greatest and least values of $\sin x \cos x$ are

Easy

View Solution

The set of all values of $\lambda$ for which the equation $\cos ^2 2x - 2 \sin ^4 x - 2 \cos ^2 x = \lambda$ has a solution is:

DifficultJEE MAIN 2023

View Solution

If $\left| \cos \theta \left\{ \sin \theta + \sqrt{\sin^2 \theta + \sin^2 \alpha} \right\} \right| \le k$,then the value of $k$ is

Difficult

View Solution

The expression $sin^{2n}x + cos^{2n}x$ lies between which of the following values?

View Solution

The maximum value of $3 \cos \theta + 5 \sin \left( \theta - \frac{\pi}{6} \right)$ for any real value of $\theta$ is

DifficultJEE MAIN 2019

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

The smallest value of $5 \cos \theta + 12$ is

Similar Questions

The greatest and least values of $\sin x \cos x$ are

The set of all values of $\lambda$ for which the equation $\cos ^2 2x - 2 \sin ^4 x - 2 \cos ^2 x = \lambda$ has a solution is:

If $\left| \cos \theta \left\{ \sin \theta + \sqrt{\sin^2 \theta + \sin^2 \alpha} \right\} \right| \le k$,then the value of $k$ is

The expression $sin^{2n}x + cos^{2n}x$ lies between which of the following values?

The maximum value of $3 \cos \theta + 5 \sin \left( \theta - \frac{\pi}{6} \right)$ for any real value of $\theta$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module