Question

How do you find the six trig ratios?

Answer 1

Use the definitions based on a right triangle with a unit length hypotenuse (see below)

Explanation:

For a general angle `theta`
`color(white)("XXXX")`Draw a right triangle such that `/_theta` is at the Cartesian origin and the right angle is on the X-axis.

`sin(theta) = "length of opposite side"/"length of hypotenuse"`

`cos(theta) = "length of adjacent side" / "length of hypotenuse"`

`tan(theta) = "length of opposite side"/ "length of adjacent side"`

`csc(theta) = 1/sin(theta)`

`sec(theta) = 1/cos(theta)`

`cot(theta) = 1/tan(theta)`

Answer 2

How to find the 6 trig ratios?

Explanation:

The 4 main trig ratios are given by the trig unit circle.
AM = x is a variable arc, and M is the terminal point that rotates counterclockwise on the trig circle. The projection of the terminal M on 4 different axis of the trig unit circle defines the 4 trig functions: cos x, sin x, tan x and cot x
On the trig unit circle,
The segment Om = sin x . Om varies between - 1 and 1.
Segment On = cos x . On varies between -1 and 1.
Segment AT = tan x . AT varies from -infinity to +infinity
Segment BU = cot x. BU varies from -infinity to +infinity