Question 1209512: Find all six trignometric functions of 𝜃 if the given point is on the terminal side of 𝜃. (If an answer is undefined, enter UNDEFINED.)
(6, 8)
Answer by CPhill(1987)   (Show Source):
You can put this solution on YOUR website! You did not provide the point. I need the coordinates of the point to calculate the trigonometric functions. However, I can show you the process with a general example.
**Example:**
Let's say the given point is (3, -4).
1. **Find 'r' (the distance from the origin to the point):**
r = √(x² + y²)
r = √(3² + (-4)²)
r = √(9 + 16)
r = √25
r = 5
2. **Calculate the Trigonometric Functions:**
* **Sine (sin θ):** y/r = -4/5
* **Cosine (cos θ):** x/r = 3/5
* **Tangent (tan θ):** y/x = -4/3
* **Cosecant (csc θ):** r/y = -5/4
* **Secant (sec θ):** r/x = 5/3
* **Cotangent (cot θ):** x/y = -3/4
**General Process:**
If you are given a point (x, y):
1. **Calculate r:** r = √(x² + y²)
2. **Calculate the functions:**
* sin θ = y/r
* cos θ = x/r
* tan θ = y/x (undefined if x = 0)
* csc θ = r/y (undefined if y = 0)
* sec θ = r/x (undefined if x = 0)
* cot θ = x/y (undefined if y = 0)
**Provide the point, and I will calculate the trigonometric functions for you.**
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