Question 1026502
answer is selection 3.


here's why.


start with 2 * cos(theta) = 5 + (6 / cos(theta) 


multiply both sides of the equation by cos(theta) to get:


2 * cos^2(theta) = 5 * cos(theta) + 6


subtract the right side of the equation from both sides of the equation to get:


2 * cos^2(theta) - 5 * cos(theta) - 6 = 0.


this is a quadratic equation.


solve it using the quadratic formula.


you will get:


cos(theta) = -.8860009 or cos(theta) = 3.3860009


since cos(theta) has to be less than 1 or greater than -1, cos(theta) = 3.3860009 is not valid.


the only solution is cos(theta) = -.8860009.


the cosine function is negative in quadrants 2 and 3.


it is positive in quadrants 1 and 4.


to find the equivalent angle in quadrant 1, make the cosine positive.


you will get cos(theta) = .8860009.


solve for theta to get theta = arccos(.8860009) = 27.6250548 degrees.


the equivalent angle in the second quadrant is 180 degrees minus that.


the equivalent angle in the third quadrant is 180 degrees plus that.


you will get:


theta = 152.3749452 in the second quadrant and theta = 207.6250548 in the third quadrant.


round to nearest tenth of a degrees and you get:


theta = 152.4 in the second quadrant and theta = 207.6 in the third quadrant.


that agrees with selection 3.


find cos(152.4) with your calculator and you will see that it is equal to -.886.....


find cos(207.6) with your calculator and you will see that it is equal to -.886... as well.


the calculator confirms that the angles are correct.