Question

Greatest value of minus 5sin theta plus 12cos theta

Answer 1

You have to use the formula (a^2+b^2)^1/2 where

a,b are the coefficients of cosine and sine functions respectively.
= √[(-5)^2 + (12)^2 ]
= 13

Answer 2

$The \ greatest \ value \ of -5\sin\theta +12\cos\theta \ is \ 13$

Given:

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

Solution:

To find a greatest value of a function of type $f(\theta)=a \sin \theta+b \cos \theta$ is done by the formula $\sqrt{a^{2}+b^{2}}$

Where 'a' and 'b' symbolize a coefficient of functions.

We have to find the value of $(-5 \sin \theta+12 \cos \theta)$,

$\Rightarrow \sqrt{5^{2}+12^{2}}$

$\Rightarrow \sqrt{25+144}$

$\Rightarrow \sqrt{169}$

$\Rightarrow 13$

$So, \ the \ value \ of (-5 \sin \theta+12 \cos \theta) \Rightarrow 13$