Question

Suppose that θ is in standard position and the given point is on the terminal side of θ. Give th value of the indicated trig function for θ. 6) (−5,12) : Find sinθ.

A) − 13/12
B) 13/5
C) = 13/5
​D) 13/12

Answer 1

To find sinθ for the given point (-5, 12), we use the definition of sinθ in a right triangle and apply the Pythagorean theorem to find the hypotenuse. Then we divide the opposite side length by the hypotenuse length to find the value of sinθ.

Step-by-step explanation:

To find the value of sinθ for the given point (-5, 12), we need to use the definition of sinθ in a right triangle. Let's draw a right triangle with the given point as one of its vertices. The x-coordinate of the point (-5) represents the adjacent side of θ, and the y-coordinate (12) represents the opposite side. We can use the Pythagorean theorem to find the hypotenuse, which is the square root of the sum of the squares of the lengths of the other two sides.

Therefore, the length of the hypotenuse is √((-5)^2 + 12^2) = √(25 + 144) = √169 = 13.

Now, we can find sinθ by dividing the length of the opposite side (12) by the length of the hypotenuse (13). So, sinθ = 12/13 = 13/5.