Evaluate sin(theta) and cosine (theta) for the angle theta
The graph gives you a point of (0.6,-0.8) on the x y coordinate plane with a radius of what appears to be 1 ( unit circle )
sin (theta) =
cos (theta) =
as usual,
sinθ = y/r
cosθ = x/r
You know x,y,r so get the functions
To evaluate sin(theta) and cosine(theta) for the angle theta, we can use the coordinates of the point on the unit circle. In this case, the point is (0.6, -0.8).
Since the point is on the unit circle, the distance from the origin to the point is 1. Therefore, the radius is indeed 1.
To find sin(theta), we look at the y-coordinate of the point. In this case, sin(theta) = -0.8.
To find cosine(theta), we look at the x-coordinate of the point. In this case, cos(theta) = 0.6.
So, sin(theta) = -0.8 and cos(theta) = 0.6.
To evaluate sin(theta) and cos(theta) for an angle theta, we can use the coordinates of a point on the unit circle where the angle intercepts the circle.
Given the point (0.6, -0.8) on the xy-coordinate plane, we can determine the radius, which is the distance of the point from the origin (0,0). In this case, it appears to be 1.
Using the Pythagorean theorem, we can calculate the radius:
radius = sqrt((0.6)^2 + (-0.8)^2)
radius = sqrt(0.36 + 0.64)
radius = sqrt(1)
radius = 1
Now that we know the radius is 1, we can determine the values of sin(theta) and cos(theta) by looking at the coordinates.
For sin(theta), we use the y-coordinate of the given point, which is -0.8. Since the radius is 1, sin(theta) = y-coordinate / radius.
sin(theta) = -0.8 / 1
sin(theta) = -0.8
Therefore, sin(theta) = -0.8.
For cos(theta), we use the x-coordinate of the given point, which is 0.6. Again, since the radius is 1, cos(theta) = x-coordinate / radius.
cos(theta) = 0.6 / 1
cos(theta) = 0.6
Therefore, cos(theta) = 0.6.
In summary:
sin(theta) = -0.8
cos(theta) = 0.6