What are the solutions of the equation?

Question

What are the solutions of the equation secxcotx = −2 on the interval [0,2π)?

Select all of the correct solutions:

Answer choices:

π6 , π4 , π3 , π2 , 2π3 , 3π4 , 5π6 , π , 7π6 , 5π4 , 4π3 , 3π2 , 5π3 , 7π4 , 11π6

Answer 1

The easiest way to do this problem is to realize that except where cos x = 0,

sec x cot x = 1/sin x. Your problem wants to know where sin x = -1/2.

sin x = 1/2 occurs when x = 30° and you should know the mnemonic AllSinTanCos to tell you which function is positive in which quadrant....you want the answer to be in quadrants III and IV.

5:09 PM 6/9/2020

I don't know how you got all those answers of which only 2 are correct: 7π/6 and 11π/6.

Perhaps you didn't check the sin of each of your answers.

It would probably help if you would draw a figure: on the co-ordinate axes draw a line through the origin at 30° and a similar one at 150° (so that you have an x on the axes.

The answers should now be obvious to you.