Question : If $r\sin\theta=\frac{7}{2}$ and $r\cos\theta=\frac{7\sqrt3}{2}$, then the value of $\theta$ is:

Option 1: 30°

Option 2: 45°

Option 3: 60°

Option 4: 75°

Question : If $\sin ^2 \theta-3 \sin \theta+2=0$, then find the value of $\theta\left(0^{\circ} \leq \theta \leq 90^{\circ}\right)$.

Option 1: 45°

Option 2: 0°

Option 3: 60°

Option 4: 90°

Question : If $\theta$ is positive acute angle and $7\cos^{2}\theta+3\sin^{2}\theta =4$, then the value of $\theta$ is:

Option 1: $60^{\circ}$

Option 2: $30^{\circ}$

Option 3: $45^{\circ}$

Option 4: $90^{\circ}$

Question : The value of $\theta$ $ \left ( 0\leq \theta \leq 90^{\circ} \right )$ satisfying $2\sin^{2}\theta = 3\cos \theta$ is:

Option 1: $60^{\circ}$

Option 2: $30^{\circ}$

Option 3: $90^{\circ}$

Option 4: $45^{\circ}$

Question : For any acute angle $\theta, \sin \theta+\sin^2 \theta=1$, then the value of $\cos^2 \theta+\cos^4 \theta=$___________.

Option 1: 0

Option 2: 1

Option 3: 2

Option 4: –1