86.5k views
4 votes
Find the value for sin θ given the point (-3, 4) on the terminal side. Leave your answer in fraction form.

User Jimmt
by
7.1k points

1 Answer

5 votes

Answer:

sin θ = 4/5

Explanation:

The Pythagorean theorem tells you the distance (h) from the origin to the terminal point:

h² = (-3)² +(4)² = 25

h = 5 . . . . . . . . take the square root

The mnemonic SOH CAH TOA reminds you ...

Sin = Opposite/Hypotenuse

For angles other than 1st-quadrant angles, it can sometimes be difficult to identify the relevant sides of the relevant triangle. If the angle were a 1st-quadrant angle, it would be clear that the side opposite the angle is the y-coordinate of the point on the terminal side. That remains the case for all angles. The hypotenuse is always the positive distance from the origin to the terminal point.

So, you have

sin θ = opposite/hypotenuse = 4/5

Find the value for sin θ given the point (-3, 4) on the terminal side. Leave your-example-1
User Simon Ludwig
by
6.7k points
Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.