CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon


Question

Range of $$ 5\displaystyle \cos\Theta+3\cos(\Theta-\frac{\pi}{3})+8$$ 


A
[7,1]
loader
B
[1,8]
loader
C
[1, 15]
loader
D
[2, 15]
loader

Solution

The correct option is B [1, 15]
$$\displaystyle f(\theta )=5 cos \theta +3 cos (\theta - \frac{\pi }{3})+8$$
$$\displaystyle =5 cos \theta +3 [cos \theta cos \frac{\pi }{3} -sin \theta sin \frac{\pi }{3}]+8$$
$$\displaystyle =5 cos \theta +\frac{3}{2}[cos \theta -sin \theta ]+8$$
$$\displaystyle f(\theta )=\frac{13 cos \theta -3 sin \theta +16}{2}$$
range of $$13 cos \theta -3 sin \theta \epsilon [-\sqrt{169+9} , \sqrt{169+9}]$$
$$\epsilon [-\sqrt{174} , \sqrt{174}]$$
$$16 \leq \sqrt{174} \leq 17$$
$$\therefore $$ range of $$\displaystyle f(\theta )\epsilon [\frac{16-\sqrt{174}}{2} , \frac{16+\sqrt{174}}{2}]$$
$$[1,15]$$ is a part of $$\displaystyle [\frac{16-\sqrt{174}}{2} , \frac{16+\sqrt{174}}{2}]$$

Maths

Suggest Corrections
thumbs-up
 
0


similar_icon
Similar questions
View More


similar_icon
People also searched for
View More



footer-image