please solve this problem: please solve the trigonometric equation
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give all positive values of the angle between 0 to 360 degress
give any approximate value to the nearest minute only.
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Multiply the equation through by LCD = 4
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Simplifying:
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Use the identity cos 2q = 1 - 2sinq
to substitute 1 - 2sinx for cos(2x) in the first term:
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Remove the parentheses by distributing:
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Combine like terms:
=
=
=
=
Take the square roots of both sides:
=
=
Find the inverse sine of .836600265 in the
first quadrant:
= 56.78908924
To change the decimal part of that to minutes,
multiply the decimal part .78908924 by 60, getting
47.34535435' then round to the nearest minute, so
the value of x is the first quadrant is 5647'.
But since the can be positive or
negative, we will get all the angles in all the
quadrants which have 5647 as their reference
angles.
The second quadrant answer is found by
subtracting 5647' from 180 or
180 - 5647' = 17960' - 5647' = 12313'
The third quadrant answer is found by
adding 5647' to 180 or
180 + 5647' = 23647'
The fourth quadrant answer is found by
subtracting 5647' from 360
360 - 5647' = 35960' - 5647' = 30313'
So all the answers for x between 0 and 360 are
x = 5647', 12313', 23647', and 30313
Edwin