How do you find the angle of sin theta = 1/2 (square root 2)? (note: the angle is >50*)
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Anonymous
ANSWERS: 2
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So, the sin of the angle is 1/2*sqrt(2) and you want the angle? Simply find 1/2 the square root of 2, about 0.70710678118654752440084436210485. To find the angle, use arc sine, should be found on any scientific calculator. I can tell you just by looking at it that the angle was 45º (if you use a calculator). But since the angle is greater than 50, you must find the next angle whose sine value is 0.707. Sine never ends, so it could be 405, 765, 1125... However, people rarely label angles as being 405º because it's identical to 45º.
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If you use a scientific calculator to take the inverse sine of (1/2)√(2), you will find that the angle θ = 45° but the sine function repeats itself in the second quadrant to find this angle subtract the angle that the calculator gave you from 180° as follows: 180° - 45° = 135° Double check your answer by entering 135 into your calculator and then hit the "sin" key; you will get 0.707...
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