Important trig

Question 1

1 + tan²x = ?

Answer 1

1 + tan²x = sec²x

Question 2

cos²x + sin²x = ?

Answer 2

cos²x + sin²x = 1

Question 3

sin2x = ?

Answer 3

sin2x = 2sinxcosx

Question 4

cos2x = ?

Answer 4

cos2x = cos²x - sin²x

= 2cos²x - 1

= 1 - 2sin²x

Question 5

1/cos =

1/sin =

1/tan =

Answer 5

1/cos = sec

1/sin = cosec

1/tan = cot

Question 6

sinhx =

coshx =

tanhx =

Answer 6

sinhx = (e^x - e^-x) / 2

coshx = (e^x + e^-x) / 2

tanhx = (e^x - e^-x) / (e^x + e^-x)

Question 7

Derivative of sinh = ?

Derivative of cosh = ?

Derivative of tanh = ?

Answer 7

Derivative of

sinh <=> cosh

Derivative of tanh = sech²

Question 8

What are the steps to differntiating inverse trig functions?

Answer 8

1. Eliminate the inverse
2. Differentiate wrt x (usually means add a dy/dx)
3. Rearrange for dy/dx
4. Get the RHS in terms of x.

Question 9

Name the missing lengths and angles.

Answer 9

Question 10

Name the missing lengths and angles.

Answer 10

Question 11

What is the domain of:

arcsin?

arcos?

Answer 11

The domain of arcsin is the domain where sin is one-one, therefore -π/2 to π/2.

The domain of arcsin is the domain where sin is one-one, therefore 0 to π.

Question 12

What is dy/dx of an inverse function f^-1(x)?

Answer 12

dy/dx = 1/ f (f^-1(x))

Remember if f(x) = 0 then f^-1(0) = x