SOLUTION: Solve the following equation for {{{ 0 }}} &#8804; x < 360. {{{ 3 }}}csc(x) + {{{ 5 }}} = csc(x) + {{{ 9 }}} A.) {{{ 30 }}}° & {{{ 150 }}}° B.) {{{ 150 }}}° and {{{ 330 }}}°

Algebra ->  Trigonometry-basics -> SOLUTION: Solve the following equation for {{{ 0 }}} &#8804; x < 360. {{{ 3 }}}csc(x) + {{{ 5 }}} = csc(x) + {{{ 9 }}} A.) {{{ 30 }}}° & {{{ 150 }}}° B.) {{{ 150 }}}° and {{{ 330 }}}°      Log On


   

Question 1064092: Solve the following equation for +0+ ≤ x < 360.
+3+csc(x) + +5+ = csc(x) + +9+
A.) +30+° & +150+°
B.) +150+° and +330+°
C.) +60+° & +120+°
D.) +120+° and +300+°
Thanks!
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
3%2Acsc%28x%29%2B5+=+csc%28x%29%2B9 Start with the given equation


3%2Acsc%28x%29%2B5-5+=+csc%28x%29%2B9-5 Subtract 5 from both sides


3%2Acsc%28x%29+=+csc%28x%29%2B4 Combine like terms


3%2Acsc%28x%29-csc%28x%29+=+csc%28x%29%2B4-csc%28x%29 Subtract csc(x) from both sides


2csc%28x%29+=+4 Combine like terms


%282csc%28x%29%29%2F2+=+4%2F2 Divide both sides by 2


csc%28x%29+=+2 Reduce


1%2F%28sin%28x%29%29+=+2%2F1 Rewrite csc(x) in terms of sine. Rewrite the "2" on the right side as "2/1"


sin%28x%29+=+1%2F2 Apply reciprocals to both sides


The goal now is to solve sin%28x%29+=+1%2F2 or sin%28theta%29+=+1%2F2


Use a unit circle to find points on the unit circle that have a y coordinate of y = 1/2. This happens at theta = 30 and theta = 150 (in Q1 and Q2 respectively)

So that means x = 30 or x = 150 (where x is the angle in degrees).


The final answer is Choice A) 30 degrees and 150 degrees