Question 198281: I am having a very hard time will sin and cos problems. Here is one that I can't solve:  .I don't even know how to start because I haven't had any training in cos and sin problems yet. I just know that this problem will have four answers. If you have any advice on the cos and sin problems I would love to hear it. Thank you!
Answer by RAY100(1637)   (Show Source):
You can put this solution on YOUR website! sin(2x-pi/3) =1/2
.
this is a complicated problem, even for those who study trig
.
in a right triangle, sin is the opposite side divided by hypotenuse
.
of note sin function is positive in quadrants 1 &2, that is angles less than 180 degrees.
.
pi / 3 is radians for 180 /3 = 60 degrees, lets use degrees
.
to get started LET y = (2x-pi/3) = (2x -60 degrees)
.
sin y = .500
.
using arc sign (inverse), y = 30 degrees, or 150 degrees.
.
This is found on the calculator by using the second function key and the sign.
check by finding sin 30 and sign 150
.
getting 150 is another story, it is the complement (180 -30) of 30 degrees that is positive.
other complements are (30 +180 =210) or (360-30 = 330) ,,,both are negative however
.
getting back to main problem, y = 30 and / or 150
.
substituting back,,, (2x -60) = 30,,,,,,(2x-60) = 150
.
2x =90 ,,,,,2x = 210
.
x=45,,, x=105,,,,,,degrees
.
checking answer
.
for x=45, sin(2(45) -60) = .5,,,sin (30) = .5,,,ok
.
for x=105, sin ( 2(105) -60) = .5 ,,,sin (150) =.5,,,ok
.
This might take some study, do not despair
|
|
|
