Question

Calculate the value of $\sqrt{\frac{9{\sin }^2\theta +9{\cos }^2\theta }{4}}$.

• A. $1.5$
• B. $2.25$
• C. $8.9$
• D. $23.1$

Answer 1

Answer: (A)

$1.5$

Trigonometric identity $:{\sin }^2\theta +{\cos }^2\theta =1$

$\sqrt{\frac{9{\sin }^2\theta +9{\cos }^2\theta }{4}}=\sqrt{\frac{9{(\sin }^2\theta +{\cos }^2\theta )}{4}}$

$=\sqrt{\frac{9\times 1}{4}}$

$=\frac{3}{2}$

$=1.5$