find the value of sin theta for angle theta in standard position if point with coordinates (negtive 3, 2) lies on its terminal side. i had 2 over sqrt 13 but it was wrong please correct.
Beats me. I get the same 2/sqrt 13
Same here, bro
To find the value of sin(theta) for an angle in standard position, we need to use the coordinates of the point on the terminal side of the angle.
In this case, you mentioned that the point has coordinates (-3, 2).
To find sin(theta), we need to calculate the ratio of the y-coordinate of the point to the length of the radius. The length of the radius is the distance from the origin (0,0) to the point (-3, 2).
Using the distance formula, we can find the length of the radius:
r = sqrt[(-3 - 0)^2 + (2 - 0)^2]
= sqrt[(-3)^2 + (2)^2]
= sqrt[9 + 4]
= sqrt[13]
Now, we can calculate sin(theta) by dividing the y-coordinate by the length of the radius:
sin(theta) = y-coordinate / length of the radius
= 2 / sqrt[13]
= 2sqrt[13] / 13
Thus, the correct value of sin(theta) for the given point (-3, 2) is 2sqrt[13] / 13.