Question

Consider the angle in standard position whose measure is radians. The terminal side of this angle is in the third quadrant and lies on the line given by y=10x. Find sin and cos.

Answer 1

The nice thing is that the equations for sin and cosine automatically take into the signs involved.

consider the point (-1,-10) in the third quadrant. h = sqrt(101) and is always positive

sin = y/h = -10/sqrt(101) = -0.995
cos = x/h = -1/sqrt(101) = -0.0995

Answer 2

Sin therapists divide by 2

Answer 3

Sin theta divide by 2

Answer 4

[AI-generated answer — Explain Bot]

To find the sin and cos of an angle in standard position, we need to determine the x and y coordinates of the point where the terminal side of the angle intersects the unit circle.

In this case, we are given that the terminal side of the angle is in the third quadrant and lies on the line y = 10x.

To find the x-coordinate of the point, we can equate the given line equation with the x-coordinate. Let's set y equal to zero:
0 = 10x
This implies x = 0.

So, the x-coordinate of the point where the terminal side intersects the unit circle is 0.

To find the y-coordinate, we can substitute the x-coordinate into the given line equation:
y = 10(0)
y = 0.

Therefore, the y-coordinate of the point is also 0.

Now, we have the coordinates (x, y) of the point where the terminal side intersects the unit circle: (0, 0).

Next, we can use these coordinates to find the sin and cos of the angle. Recall that the sin of an angle is equal to the y-coordinate of the point on the unit circle, and the cos of an angle is equal to the x-coordinate.

In this case, since both the x and y coordinates of the point are 0, we have:
sin(angle) = y-coordinate = 0
cos(angle) = x-coordinate = 0

Therefore, the sin and cos of the given angle in standard position are both equal to 0.