If (96,2) is a point on the terminal side of an angle THETA in standard position, what is the value of sin THETA?
How do i do this?
Draw a right triangle by drawing a line from the point to the x axis. Then sin(theta) = opposite / hypotenuse.
To find the value of sin THETA, we need to determine the ratio of the length of the side opposite the angle to the length of the hypotenuse.
In this case, we are given the point (96,2) on the terminal side of the angle. This means we can form a right triangle with the x-axis as the adjacent side and the y-axis as the opposite side. The distance from the origin (0,0) to the point (96,2) represents the hypotenuse.
Step-by-step:
1. Draw the x-axis and y-axis on a coordinate plane.
2. Plot the point (96,2) on the coordinate plane.
3. Draw a line connecting the origin (0,0) to the point (96,2).
Now, we have a right triangle with the y-axis as the opposite side (having a length of 2), the x-axis as the adjacent side (also called the base, having a length of 96), and the line we drew as the hypotenuse.
To find the value of sin THETA, we divide the opposite side length by the hypotenuse length:
sin THETA = opposite/hypotenuse = 2/√(96^2 + 2^2)
Calculating the value of sin THETA:
sin THETA = 2/√(96^2 + 2^2)
= 2/√(9216 + 4)
= 2/√9216 + 4
= 2/√9216 + √4
= 2/√9220
So, the value of sin THETA is 2/√9220.