The maximum value of 3cos[ ] + 5sin [( - 6 )] for any real value of [ ] is :

Question

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

Accepted Answer

y = 3cos$$\theta $$ + 5 $$\left( {\sin \theta {{\sqrt 3 } \over 2} - \cos \theta {1 \over 2}} \right)$$

$${{5\sqrt 3 } \over 2}$$ sin$$\theta $$ + $${1 \over 2}$$cos$$\theta $$

ymax = $$\sqrt {{{75} \over 4} + {1 \over 4}} $$ = $$\sqrt {19} $$

Solutions · 1