Question

The maximum value of $(3\sin \theta +4\cos \theta )$ is

• A. 7
• B. 5
• C. 1
• D. -1

Answer 1

The correct option is B 5

$Letuscalculatethevalueof3sin\theta +4cos\theta forstandardangles.\theta 3sin\theta +4cos\theta =0^{\circ }\to 3\times 0+4\times 1=4={30}^{\circ }\to 3\times \frac{1}{2}+4\times \frac{\sqrt{3}}{2}=4.964=5={45}^{\circ }\to 3\times \frac{1}{\sqrt{2}}+4\times \frac{1}{\sqrt{2}}=4.95=5={60}^{\circ }\to 3\times \frac{\sqrt{3}}{2}+4\times \frac{1}{2}=4.6={90}^{\circ }\to 3\times 1+4\times 0=3Sothemaximumvalueof3sin\theta +4cos\theta is5\left(AnsB\right)$