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-90^(@) <= theta <= 90^(@). Find the value of 
theta in degrees.

{:[sin(theta)=(sqrt2)/(2)],[theta=◻]:}
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90°-90^° θ\theta 90°-90^°. Find the value of θ\theta in degrees.\newline\begin{align*} \sin(\theta)&=\frac{\sqrt{2}}{2},\ \theta& = \square \end{align*}

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Q. 90°-90^° θ\theta 90°-90^°. Find the value of θ\theta in degrees.\newline\begin{align*} \sin(\theta)&=\frac{\sqrt{2}}{2},\ \theta& = \square \end{align*}
  1. Recognize trigonometric function: Step 11: Recognize the trigonometric function and its value.\newlineWe are given sin(θ)=22\sin(\theta) = \frac{\sqrt{2}}{2}. We need to find the angle θ\theta that satisfies this equation within the specified range.
  2. Recall standard angles: Step 22: Recall the standard angles for sine.\newlineThe sine of 4545 degrees (π4\frac{\pi}{4} radians) is 2/2\sqrt{2}/2. This is a well-known value from the unit circle.
  3. Determine possible values: Step 33: Determine possible values of θ\theta. Since sin(θ)=sin(45)\sin(\theta) = \sin(45^\circ), θ\theta could be 4545^\circ. Also, sine is positive in the first and second quadrants, so we also consider negative angles. However, in the range 90-90^\circ to 9090^\circ, the only angle where sine equals 2/2\sqrt{2}/2 is 4545^\circ.

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