Trig questions regrading exact values and quadrants

Question

The solution to the trig equation 4cos theta +3 =0 are in which quadrant?

 

Given csc theta = 2 sqrt3/3 and -270 degrees < theta <180 degrees

Determine the exact values of theta 

Determine the coordinates of the points on the unit circle where the terminal arm of theta intersect the unit circle

Determine the exact values of cos theta and tan theta 

 

Given the equation 6costhetasintheta-2costheta =0 

 

Solve this equation, to nearest tenth of a degree, in the domain, 0 degrees < theta < 360 degrees 

 

Determine the general solution to the equation 

Answer 1

HERE'S SOME HELP ON SOME OF YOUR PROBLEMS.

Given csc theta = 2 sqrt3/3 and -270 degrees < theta <180 degrees

 

The positioning information for θ is too broad, so I'm going to take Quadrant II because < 180^o is one of the possibilities. Usually this kind of information should nail down a single quadrant.

 

Given csc θ implies that sin θ = √3 / 2 and thus cos θ = -1/2.

If you want other quadrants, that can be done, manually. 

 

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The solution to the trig equation 4cos theta +3 =0 are in which quadrant?

 

cos  θ = -3/4 and using the inverse function gives you the one solution in Quadrant II.

Manually, you can locate another solution in Quadrant III--instead of reference angle being in II, put it into III.