Advanced Math/trig

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Expert: - 7/21/2009


Question
given: 0<or= X <360 degrees

Solve:
1) 3tan 3X- square root of 3= 0
2) 3csc X/2 - 2square root of 3= 0  

Answer
1) The problem is: 3 tan 3X  -  √3 = 0.
This can be seen to be 3 tan 3X = √3, or tan 3X = √3 / 3.
It is known that √3 = 1.7321, and when you take √3 / 3,
you get 0.5774 as the radians for 3x.
In degrees, that is 33.0797°.

Since it wants all x between 0° and 360°,
3x would be all x between 0° and 1080° since 1080 = 3*360.

Note that the tan(x) repeats in the same way every 180°,
so when 180° is divided by 3, 60° is gotten.  
The list of all of the answers is then
33.097° * 60n° for n = 0, 1, 2, 3, 4, and 5.

2) The problem is 3 csc X/2  -  2√3 = 0
That turns into csc X/2 = 2√3 / 3, or csc X/2 = 1.1547.
In degrees, that is 66.1595°.

Note that the csc(x) curve is symmetric around x = 90°.  
This means that the other angle is 90° + (90-66.1595)° = 113.8405°.
It is positive for x between 0° and 180°.

Note that X/2 is this angle,, so X is 2 * angles found.
That means X is 2*66.1595° = 132.3189 or 2*113.8405 = 227.680.

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