Question
The point (-2,7) defines an angle 𝜃 in standard position. Find sin 𝜃
Answers
Answered by
GPT 3.5
To find sin 𝜃, we need to first determine the hypotenuse, adjacent side, and opposite side of the right triangle formed by the point (-2,7) in the Cartesian plane.
The distance from the origin to the point (-2,7) is the hypotenuse, which can be found using the Pythagorean theorem:
hypotenuse = √((-2)^2 + 7^2)
hypotenuse = √(4 + 49)
hypotenuse = √53
The x-coordinate of the point (-2,7) is -2, which is the adjacent side of the triangle.
The y-coordinate of the point (-2,7) is 7, which is the opposite side of the triangle.
Now, we can find sin 𝜃 using the definition of sin in a right triangle:
sin 𝜃 = opposite/hypotenuse
sin 𝜃 = 7/√53
Therefore, sin 𝜃 = 7/√53 or sin 𝜃 = 7√53/53.
The distance from the origin to the point (-2,7) is the hypotenuse, which can be found using the Pythagorean theorem:
hypotenuse = √((-2)^2 + 7^2)
hypotenuse = √(4 + 49)
hypotenuse = √53
The x-coordinate of the point (-2,7) is -2, which is the adjacent side of the triangle.
The y-coordinate of the point (-2,7) is 7, which is the opposite side of the triangle.
Now, we can find sin 𝜃 using the definition of sin in a right triangle:
sin 𝜃 = opposite/hypotenuse
sin 𝜃 = 7/√53
Therefore, sin 𝜃 = 7/√53 or sin 𝜃 = 7√53/53.