Question

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

• A. $5$
• B. $12$
• C. $7$
• D. $17$

Answer 1

The correct option is C

$7$

Explanation for the correct answer:

Compute the required value:

Since,

$-1\le \cos \theta \le 1$

Multiplying the inequality throughout by $5$,

$-5\le 5\cos \theta \le 5$

Adding $12$

$-5+12\le 5\cos \theta +12\le 5+12$

$\Rightarrow$ $7\le 5\cos \theta +12\le 17$

$7\le 5\cos \theta +12\le 17$$7\le 5\cos \theta +12\le 17$$7\le 5\cos \theta +12\le 17$$7\le 5\cos \theta +12\le 17$

Hence the smallest value of $5\cos \theta +12$ is $7$.

Hence, option $\left(C\right)$ is the right answer.