Trig Problems: Solving for x in Sin and Cos Equations | Easy Tips and Tricks

[Short term memory]

ok i have been given a number of trig problems, and i have not taken trig for about 2 years, now i can remeber how to do the problems, but for the life of me i can't remeber how to get the answer...

ok here is the problem:
sin 2x + cos x = 0; 0<x<2 pi

here is what i got

sin 2x + cos x = 0
2 sin x cos x + cos x = 0
cos x = 0 2 sin x + 1 = 0
sin x = -1/2

here is my problem...

can some one explain to me how do i go from cos x = 0 to x = pi/2

at one point i knew this i just don't remeber... grr so frustrating...

thanks in advance

 

[Muzza]

Draw the unit circle, a point on the circle has the form (cos(a), sin(a)). Thus cos(a) is 0 precisely when... (fill in the blank ;)).

 

[Short term memory]

Muzza thanks for the response but unfortunately it made no sense to me...

but i did ask one of my roomates that just walked in the door and he said that if do cos^-1 0 i get 90 so that's pi/2 and then add 180 to 90 gives me 3pi/2 and this make sense to me,

but anyway are these answers right

x = π/2,3π/2
x = -π/6,-5π/6

but since x = -π/6,-5π/6 is not inside of 0<x<2n then the only answer are x = π/2,3π/2...

yes no or wrong?

 

[Muzza]

Well, remember that you can add any (integer) multiple of 2pi to any solution of sin(x) = -1/2 and get another solution. Thus -pi/6 + 2pi = 11pi/6 < 2pi and -5pi/6 + 2pi = 7pi/6 < 2pi are also valid solutions...

 

[Short term memory]

Well, remember that you can add any (integer) multiple of 2pi to any solution of sin(x) = -1/2 and get another solution. Thus -pi/6 + 2pi = 11pi/6 < 2pi and -5pi/6 + 2pi = 7pi/6 < 2pi are also valid solutions...

oh forgot about that thanks...

 

[K.J.Healey]

the easiest way is liek said before, the unit circle.

Imagine an X-Y axis. Draw a circle around it.
We let X = cos(theta) and Y= sin(theta)

So if you start on the X-axis, on the right, youre at 0 for Y and "1" for X (assuming the radius of the circle is 1)

The angle theta is just the angle around the circle. At (0,1) theta is 0, so we know that Cos(0) = 1 and Sin(0) = 0
If you look at 90 degrees, basically on the Y axis, we are at (1,0). So the x component, Cosine, is 0 at 90 degrees. 90 degrees is also 1/4th of a circle, which is 1/4th or 2*Pi, or Pi/2.

This is the basic idea behind a unit circle. It really helps when you use 2d vectors in physics too for projectile motion.