SOLUTION: Which of the following is a solution to sin(2x)-cosx=0? a. 60 degrees b. 90 degrees c. 120 degrees d. 240 degrees e. 300 degrees

Algebra ->  Logarithm Solvers, Trainers and Word Problems -> SOLUTION: Which of the following is a solution to sin(2x)-cosx=0? a. 60 degrees b. 90 degrees c. 120 degrees d. 240 degrees e. 300 degrees      Log On


   

Question 1170388: Which of the following is a solution to sin(2x)-cosx=0?
a. 60 degrees
b. 90 degrees
c. 120 degrees
d. 240 degrees
e. 300 degrees
Found 2 solutions by ikleyn, MathLover1:
Answer by ikleyn(52794) About Me  (Show Source):
You can put this solution on YOUR website!
.

The given equation is equivalent to


    2sin(x)*cos(x) - cos(x) = 0,   or

    
    (2sin(x)-1)*cos(x) = 0

    (sin(x) - 1/2)*cos(x) = 0.


The possible solutions are those value of x, that make at least one of the two factors equal to zero


ANSWER.  Option b), ONLY.

Solved, answered, explained and completed.



Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

sin%282x%29-cos%28x%29=0
rewrite using trig identities sin%282x%29=2sin%28x%29cos%28x%29
2sin%28x%29cos%28x%29-cos%28x%29=0
%282sin%28x%29+-1%29cos%28x%29=0
solutions:
2sin%28x%29+-1=0 ->sin%28x%29=1%2F2
or
cos%28x%29=0

if sin%28x%29=1%2F2 then sin%5E-1%281%2F2%29=30°
if cos%28x%29=0 then cos%5E-1%280%29=90°
answer: b. 90 degrees