P(2, 9) is a point on the terminal side of è in standard position. What is the exact value of tan è?
the hypotenuse must be sqrt(4+81)
tan theta=9/hypotenuse
To find the exact value of tan è, we need to use the given point (2, 9) to determine the trigonometric functions sine, cosine, and tangent.
Here's how we can do it step by step:
1. Given that the point (2, 9) lies on the terminal side of è in standard position, we can first calculate the hypotenuse, which is the distance from the origin to the point (2, 9). This can be found using the Pythagorean theorem:
hypotenuse = √(2² + 9²) = √(4 + 81) = √85
2. Next, we find the values of sine and cosine using the coordinates of the point:
sine(è) = opposite side / hypotenuse = 9 / √85
cosine(è) = adjacent side / hypotenuse = 2 / √85
3. Finally, we can calculate the tangent(è) by dividing the sine(è) by the cosine(è):
tangent(è) = sine(è) / cosine(è) = (9 / √85) / (2 / √85) = 9 / 2
Therefore, the exact value of tan è is 9/2.