If sin(theta) = -0.8 and theta is in the third quadrant of the xy plane, what is cos(theta)?
Well, in the third quadrant, all those negative angles are quite crabby. So, let's put on our clown shoes and figure this out!
We know that sin(theta) is -0.8, which makes theta a bit of a downer. To find cos(theta), we can use the Pythagorean identity: sin^2(theta) + cos^2(theta) = 1.
Since sin(theta) = -0.8, we can substitute -0.8 for sin(theta) in the equation: (-0.8)^2 + cos^2(theta) = 1.
Simplifying this, we get: 0.64 + cos^2(theta) = 1.
Now, solving for cos(theta), we subtract 0.64 from both sides: cos^2(theta) = 0.36.
Finally, taking the square root of both sides, we find that: cos(theta) = ±0.6.
Since theta is in the third quadrant, where cos(theta) is negative, we get: cos(theta) = -0.6.
So, in clown terms, we can say that cos(theta) is feeling a little negative, just like theta. They make quite the duo, don't they?
To find the value of cos(theta), we can use the Pythagorean identity:
sin^2(theta) + cos^2(theta) = 1
Since sin(theta) is given to be -0.8, we can substitute it into the equation:
(-0.8)^2 + cos^2(theta) = 1
0.64 + cos^2(theta) = 1
Subtracting 0.64 from both sides:
cos^2(theta) = 0.36
Taking the square root of both sides:
cos(theta) = ±0.6
Since theta is in the third quadrant, where the cosine function is negative, we choose the negative value:
cos(theta) = -0.6
To find the value of cos(theta), we can use the identity: sin^2(theta) + cos^2(theta) = 1
Given that sin(theta) = -0.8, we can substitute the value into the equation:
(-0.8)^2 + cos^2(theta) = 1
Simplifying this equation will allow us to find the value of cos(theta):
0.64 + cos^2(theta) = 1
Rearranging the equation to solve for cos(theta):
cos^2(theta) = 1 - 0.64
cos^2(theta) = 0.36
To find the value of cos(theta), we need to take the square root of both sides:
cos(theta) = ±√0.36
Since theta is in the third quadrant, cosine is negative there. Therefore, we take the negative square root:
cos(theta) = -√0.36
Simplifying:
cos(theta) = -0.6
Therefore, cos(theta) is equal to -0.6.
draw the triangle.
sin = y/r
cos = x/r