conditional trig equations

[Guest]

hello, Id like some help with this question

2 + csc x = 0 for 0 < orequal x < 2pi

here is what I have so far:

1/sin = -2

sin is negative in Q3 and 4, so I draw my angles with opp length -2 and hypotenuse length 1


correct answers are 7pi/6 and 11pi/6

thanks

 

[morson]

Good job so far. You've reached the equation:

sinx = -0.5

From symmetry properties, -pi/6 radians is one solution to this equation. But -pi/6 is outside the allowable solutions in this question. Realizing that there are many angles x for which the sine of x is -1/2 will help you.