SOLUTION: Solve the following equation for {{{ 0 }}} ≤ x < 360.
{{{ 3 }}}csc(x) + {{{ 5 }}} = csc(x) + {{{ 9 }}}
A.) {{{ 30 }}}° & {{{ 150 }}}°
B.) {{{ 150 }}}° and {{{ 330 }}}°
Algebra.Com
Question 1064092: Solve the following equation for ≤ x < 360.
csc(x) + = csc(x) +
A.) ° & °
B.) ° and °
C.) ° & °
D.) ° and °
Thanks!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given equation
Subtract 5 from both sides
Combine like terms
Subtract csc(x) from both sides
Combine like terms
Divide both sides by 2
Reduce
Rewrite csc(x) in terms of sine. Rewrite the "2" on the right side as "2/1"
Apply reciprocals to both sides
The goal now is to solve or
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
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