Fundamental Identities |
| Reciprocal Identities |
| sinx = 1 ÷ cscx |
cosx = 1 ÷ secx |
tanx = 1 ÷ cotx |
| cscx = 1 ÷ sinx |
secx = 1 ÷ cosx |
cotx = 1 ÷ tanx |
|
Quotient Identites |
| tanx = sinx ÷ cosx |
cotx = cosx ÷ sinx |
|
Pythagorean Identities |
| sin^2(x) + cos^2(x) = 1 |
1 + tan^2(x) = sec^2(x) |
1 + cot^2(x) = csc^2(x) |
|
Cofunction Identities |
sin(
- x) = cosx |
cos(
- x) = sinx |
| tan(
- x) = cotx |
cot(
- x) = tanx |
| sec(
- x) = cscx |
csc(
- x) = secx |
|
Even / Odd Identities |
| sin(-x) = -sinx |
cos(-x) = -cosx |
tan(-x) = -tanx |
| csc(-x) = -cscx |
sec(-x) = -secx |
cot(-x) = -cotx |
|
These identities are very important for solving identity
proofs, equations, and simplifying expressions. Identitiy
proofs proove an equation by keeping one side of the equation
the same, and simplifying the other to show that the equation
is true. |
Take the following identity as an example: |
sinxcscx = 1
We need to prove that sinxcscx is equal to 1. So, we will
simplify sinxcscx to 1.
According to the reciprocal identities, you can replace
sinx with 1 ÷ cscx:
(1 ÷ cscx)cscx = 1
Multiply:
1 = 1 |
Now let's try simplifying an expression: |
secx ÷ cscx
According to reciprocal identities, we can replace both
functions as so:
(1 ÷ cosx) ÷ (1 ÷ sinx)
(1 ÷ cosx) * (sinx ÷ 1)
The quotient identities then finish off the problem for
us, and we get one simple trig function:
sinx ÷ cosx = tanx
|
| Think you're ready? Take the
miniquiz! |
