Prove that sin(x)/cos(x) = tan(x)
using an angle of °
Inscribe a triangle inside a circle
The Pythagorean Theorem states
x2 + y2 = r2
The picture shows a right triangle
From the diagram, we know:
| sin(x) = |
| x |
| r |
| cos(x) = |
| y |
| r |
Divide sin(x) by cos(x)
| sin(x) |
| cos(x) |
| = |
| x/r |
| y/r |
Simplify the right side
| sin(x) |
| cos(x) |
| = |
| xr |
| yr |
Cancel r on the right side
| sin(x) |
| cos(x) |
| = |
| x |
| y |
tan(x) = (x/y)
| sin(x) |
| cos(x) |
| = |
| tan(x) |
Confirm using the angle of °
| sin() |
| cos() |
| ? |
| tan() |
| 0 |
| 1 |
| ? |
| 0 |
0 = 0
Final Answer
sin()/cos() = tan()
