SOLUTION: please solve this problem: please solve the trigonometric equation {{{ cos(2x)}}} - {{{sIn^2x/2 }}} + {{{3/4}}} = {{{0}}} give all positive values of the angle between 0 to 3

Algebra.Com
Question 86882: please solve this problem: please solve the trigonometric equation
- + =
give all positive values of the angle between 0 to 360 degress give any approximate value to the nearest minute only.

Answer by Edwin McCravy(20060)   (Show Source): You can put this solution on YOUR website!

please solve this problem: please solve the trigonometric equation 

 -  +  =  

give all positive values of the angle between 0 to 360 degress 
give any approximate value to the nearest minute only. 

 -  +  = 


Multiply the equation through by LCD = 4

 -  +  =  

Simplifying:

 -  +  = 

Use the identity cos 2q = 1 - 2sinq

to substitute 1 - 2sinx for cos(2x) in the first term:

 -  +  = 

Remove the parentheses by distributing:

 -  +  = 

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


RELATED QUESTIONS

please solve this problem: please solve trigonometric equation 3sin theta-4 cos theta = 2 (answered by vertciel)
please help me solve this: give all positive values of angle between 0 degress and 360... (answered by stanbon)
solve cos 2x-2 sin^2x +2 = 0 for ALL values of... (answered by lwsshak3)
Can you help me solve this problem please? Thank you. Use the given function values and... (answered by Solver92311)
Please help me solve this values for me. Find all values of theta in the interval 0 <... (answered by stanbon)
Please solve and give all the steps for this problem: (-2x)/(x+2) + (x)/(3) +... (answered by Susan-math)
solve. Give all positive values of the angle between 0degrees and 360degrees. Give any... (answered by Edwin McCravy)
Please help me solve this question: If sin theta = -7/25 and cos theta < 0, find the... (answered by lwsshak3)
Solve for all values of x in the interval [0, 2𝜋] that satisfy the equation. 4... (answered by ikleyn)