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Why does sin^2 (x)= 1/2 have four answers of .785r, 2.36r...
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Dr.Robert
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Why does sin^2 (x)= 1/2 have four answers of .785R, 2.36R, 3.93R, and 5.50R? I don't understand how they got any of those four answers.
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Responses
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In a plane when two lines perpendicular to each other intersects, then the plane gets divided into four parts. These four parts are known as the Quadrants.
The point where two lines intersect is the centre. We calculate the distance from the centre of different points in the quadrants. The position of points in the different quadrants are :
first quadrant => x & y both are positive
second quadrant => x is negative & y is positive
third quadrant => x & y both are negative
fourth quadrant => x is positive & y is negative |
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Winpossible
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Sep 10, 10 08:05AM PST
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Thank you. Can you tell me what I would feed into the calculator to get those four answers? I don't have a clue. Appreciate your time and expertise.
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by
RobertG
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Sep 10, 10 08:22AM PST
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More to this solution:
As in this question sin^2 = 1/ 2
=> sin x = under root of 1/2= 0.7071
so x would be
x = sin^(-1) 0.7071 = 45 degree
As you need answer in the radian, so we will convert 45 degree into radian using this formula
radian = degree * Pi/180 , where Pi = 22/7
so, using this x would be 0.785 Radian
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Winpossible
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Sep 10, 10 10:19AM PST
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More to the above answer:
Now, you have to understand some trigonometric properties of changing the quadrants,if x is an angle in the first quadrant then:
Case 1: For quadrant 2
sin ( 90 + x) = cos x = Under-root of ( 1 – sin^2 x)
Putting the value of x= 45 degree
Sin ( 90 + 45) = Under-root of ( 1 – sin^2 45) = Under-root of (1/2) = 0.7071 = sin 45
So, x = 90 + 45 degree is also an answer. This is equivalent to 2.36 radian.
Case 2 : For quadrant 3
sin ( 180 + x) = - sin x
=> sin^2 (180 + x) = sin^2 x
Putting the value of x = 45 degree
Sin (180 + 45) = 0.7071 = sin 45
So, x = 180 + 45 degree is also a answer. This is equivalent to 3.93 radian.
Case 3 : For quadrant 4
sin ( 270 + x) = - cos x =
=> sin^2 (270 + x) = cos^2 x = 1 -sin^2 x
Putting the value of x = 45 degree
=> sin^2 (270 + 45) = 0.7071 = sin^2 45
So, x = 270 + 45 degree is also an answer. This is equivalent to 5.50 radian.
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Winpossible
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Sep 10, 10 10:23AM PST
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For finding it on calculator:
1. You first need to change the mode of your calculator from degree to radian.
2. Now you have to find under-root of 1/2 using the root button on the calculator.
3. Press 2nd function on your calculator then press sin button for the under-root of 1/2, this will give you the answer of sin^-1(0.7071).
Final output on your calculator will be 0.785 radian.
Now for calculating other 3 answers, you have to manually add radian equivalents of ( 90 degree, 180 degree and 270 degree) ie( 1.575 R, 3.15 R and 4.725 R), as this is explained in the above solution.
(1) 0.785 R + 1.575 R = 2.36 R
(2) 0.785 R + 3.15 R = 3.93 R
(3) 0.785 R + 4.725 R = 5.50 R
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by
Winpossible
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Sep 10, 10 10:39AM PST
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