Question
Evaluate the expression without using a calculator. \[ \arcsin \left(\frac{\sqrt{2}}{2}\right) \]
Ask by Cross Dunn. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The angle is π/4.
Solution
We need to find the angle whose sine is (√2)/2. Recall that sin(π/4) = (√2)/2 and that the range of arcsin is [-π/2, π/2]. Since π/4 falls within this interval, we have:
arcsin((√2)/2) = π/4.
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Simplify this solution Mind Expander
The value of \( \arcsin \left(\frac{\sqrt{2}}{2}\right) \) refers to the angle whose sine is \( \frac{\sqrt{2}}{2} \). Recall the special angles in trigonometry: - The sine of \( \frac{\pi}{4} \) radians (or 45 degrees) is \( \frac{\sqrt{2}}{2} \). Therefore, we have: \[ \arcsin \left(\frac{\sqrt{2}}{2}\right) = \frac{\pi}{4} \] So the final answer is: \[ \frac{\pi}{4} \]
