Trigonometric functions

What is the value of sin(0)?

0

What is the value of tan(0)?

0

What is the value of cos(0)?

1 - ( ½ x 0² ) = 1

What is the Pythagorean identity involving sine and cosine?

sin² + cos² = 1

tan² + 1 equals what expression?

sec²

cot² + 1 equals what expression?

cosec²

What is the double angle formula for sin(2x)?

sin(2x) = 2sin(x)cos(x)

What is the double angle formula for cos(2x)?

cos(2x) = cos²(x) - sin²(x) = 1 - 2sin²(x) = 2cos²(x) - 1

What is the formula for tan(2x)?

tan(2x) = 2tan(x) / (1 - tan²(x))

What is the sine addition formula?

sin(a ± b) = sin(a)cos(b) ± cos(a)sin(b)

What is the cosine addition formula?

cos(a ± b) = cos(a)cos(b) -/+ sin(a)sin(b)

What is the tangent addition formula?

tan(a ± b) = (tan(a) ± tan(b)) / (1 -/+ tan(a)tan(b))

What is the derivative of tan(x)?

(dy/dx) tan = sec²

What is the integral of sec²?

∫ sec² = tan

What is the derivative of cot(x)?

(dy/dx) cot = -cosec²

What is the integral of cosec²?

∫ cosec² = -cot

What is the derivative of cosec(x)?

(dy/dx) cosec = -cot(cosec)

What is the integral of cosec cot?

∫ cosec cot = -cosec

What is the derivative of sec(x)?

(dy/dx) sec = sec(x)tan(x)

What is the integral of sec(x)tan(x)?

∫ sec(x)tan(x) = sec(x)

What’s the integral of sec(x)?

ln [ sec(x) + tan(x) ]

What’s the integral of cosec(x)?

ln [ cosec(x) + cot(x) ]

What’s the integral of tan(x)?

- ln [ cos(x) ]

What’s the integral of cot(x)?

ln [ sin(x) ]