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Question: If \(\theta = - \frac{\pi}{2}\)=1 and \(\theta = \frac{\pi}{4}\)then the smallest positive values of...

If θ=π2\theta = - \frac{\pi}{2}=1 and θ=π4\theta = \frac{\pi}{4}then the smallest positive values of A and B are.

A

rr

B

sinθ=12\sin\theta = \frac{1}{2}

C

32- \frac{3}{2}

D

\because

Answer

rr

Explanation

Solution

p=2mπλ,p = \frac{2m\pi}{\lambda}, and sin(πx2)=2ππ/2=4\sin\left( \frac{\pi x}{2} \right) = \frac{2\pi}{\pi/2} = 4

cos(πx2)=2ππ/2=4\cos\left( \frac{\pi x}{2} \right) = \frac{2\pi}{\pi/2} = 4\therefore and sinπx2+cosπx2=\sin\frac{\pi x}{2} + \cos\frac{\pi x}{2} = sinπx2=2ππ/2=4\sin\frac{\pi x}{2} = \frac{2\pi}{\pi/2} = 4 cosπx3=2ππ/3=6\cos\frac{\pi x}{3} = \frac{2\pi}{\pi/3} = 6.