Trig Identities

Sinx

1/cscx

Cscx

1/sinx

Cosx

1/secx

Secx

1/cosx

Tanx

1/cotx

Cotx

1/tanx

Tanx

Sinx/Cosx

Cotx

Cosx/Sinx

Sin²x+Cos²x

1

Tan²x+1

Sec²x

1+cot²x

Csc²x

Sin(-x)

-sin(x)

Csc(-x)

-Cscx

Cos(-x)

Cosx

Sec(-x)

Secx

Tan(-x)

-Tanx

Cot(-x)

-Cotx

The find all values of cos

Add 2Πk

To find all values for sin

Add Πk

When you take the square root for all trig identities

You take the negative and positive of the square root

sin2x

2sinxcosx

cos2x

cos²x - sin²x, 1 - 2sin²x, 2cos²x - 1

tan2x

1 - tan²x

sin(a + b)

sinacosb + sinbcosa

sin(a - b)

sinacosb - sinbcosa

cos(a + b)

cosacosb - sinasinb

cos(a - b)

cosacosb + sinasinb

tan(a + b)

(tana + tanb)/(1 - tanatanb)

tan(a - b)

(tana - tanb)/(1 + tanatanb)

Why are sin² and cos² considered complementary identities?

Based on the root identities Sinx = Cos(90-x) and Cosx = Sin(90-x), when you square sin and cosine you get Sin²x = Cos²(90-x) and Cos²(x) = Sin²(90-x).

Domain and Range of Sin²x and Cos²x

Domain is (-∞, ∞) and Range is [0, 1]

Graphically, why does