Trig Identities

What is the main Pythagorean trig identity?

sin²x + cos²x = 1

Simplify: sin²(x) + cos²(x)

1

Simplify: 1 - sin²(x)

cos²x

Simplify: 1 - cos²(x)

sin²x

Rewrite sin²(x)

1 - cos²x

Rewrite cos²(x)

1 - sin²x

Rewrite tan(x)

sinx/cosx

Rewrite cot(x)

cosx/sinx

Rewrite sec(x)

1/cosx

Rewrite csc(x)

1/sinx

Rewrite cot(x)

1/tanx, wherever both expressions are defined

What is d/dx[sin(x)]?

cosx

What is d/dx[cos(x)]?

-sinx

What is d/dx[tan(x)]?

sec²x

What is d/dx[cot(x)]?

-csc²x

What is d/dx[sec(x)]?

secxtanx

What is d/dx[csc(x)]?

-cscxcotx

Which three basic trig derivative formulas have a leading minus sign?

derivatives of cosx, cotx, and cscx

Simplify: -(cos(x))(-cos(x))

cos²x

Expand: (-sin(x))(1 - sin(x))

-sinx+ sin²x

Simplify: -sin(x) + sin²(x) + cos²(x)

1 - sinx

Simplify: (1 - sin(x))/(1 - sin(x))²

1/(1 - sinx)