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