the terminal side of angle theta in standard position lies on the line that travels through point (9,1), find sin of theta, cos of theta, tan of theta. (give exact values)

I will be happy to check your work. Find the the distance first to 9,1

To find the sin, cos, and tan of angle theta, we need to determine the coordinates of the terminal point of angle theta, which lies on the line passing through point (9, 1).

Since the line goes through point (9, 1), we can consider this point as the coordinates of the terminal point of angle theta. In other words, the x-coordinate is 9, and the y-coordinate is 1.

To find the values of sin(theta), cos(theta), and tan(theta), we can utilize the trigonometric relationships in a right triangle.

First, we need to find the length of the hypotenuse (r) using the given coordinates. We can use the Pythagorean theorem:

r^2 = x^2 + y^2

Substituting the x and y values, we get:

r^2 = 9^2 + 1^2
= 81 + 1
= 82

Taking the square root of both sides:

r = √82

Now that we know the value of the hypotenuse (r), we can determine the sine, cosine, and tangent of angle theta.

sin(theta) = y / r = 1 / √82 (exact value)
cos(theta) = x / r = 9 / √82 (exact value)
tan(theta) = y / x = 1 / 9 (exact value)

Therefore, the exact values for sin(theta), cos(theta), and tan(theta) are as follows:

sin(theta) = 1 / √82
cos(theta) = 9 / √82
tan(theta) = 1 / 9