Solving Trigonometric Inequalities

In which of the following intervals does the trig inequality csc(x)> -sec(x) always hold true?

A 0< x < pi/2 radians

To help solve the trig inequality 2sin(x) is greater than or equal to -1, which two equations can be graphed?

B

Which of the following is part of the solution to the trig inequality 3-tan(x) is greater than or equal to 4- 2tan(x) over the interval 0 is less than or equal to x which is less than or equal to 2pi radians?

B x= pi/3

To solve the trig inequality sec(x/3) + 4 > 2-sec(x/3), which two equations could you graph?

B y= sec(x/3) and y= -1

The graph below can be used to help solve which of the following trigonometric inequalities over the interval zero is less than or equal to x which is less than or equal to 2pi radians? (answer works for both Qs)

B: 5sin(x)- 7.5 is greater than or equal to 6sin(x)-7 OR B: cos(x)- sin(x) is greater than or equal -1

Which quarters of the unit circle satisfy the trigonometric inequality tan theta is less than or equal to 0 ? Assume that theta is the angle made by the positive x-axis and a ray from the origin

C the top left and bottom right quarters

Which half of the unit circle satisfies the trig inequality cos theta is greater than or equal to 0? Assume that theta is the angle made by the positive x-axis and a ray from the origin

C: the right half

What is the solution to the trig inequality 2-3 csc(x) > 8 over the interval 0 is less than or equal to x which is less than or equal to 2pi radians?

D pi< x< 7pi/6 and 11pi/6 < x< 2pi

Carl and Shelley are solving trig inequalites

NOT A: the points of intersection of Carl's graph have different x-coordinated than the points of intersection of Shelley's graph and different y-coordinates

Tracey is solving a trig inequality question

NOT D: there are an infinite number of solutions because the graph of the equation y= 2sin^2 (x) + cos(2x)-2 is the same as the graph of the equation y= -1, so y= 2sin^2 (x) -2 is never below y= -1