# A-Level Maths | Trigonometry (Year 13)

## Radians

- 180 degrees = pi radians
- 360 degrees = 2 pi radians
- 90 degrees = 1/2 pi radians
- To convert degrees to radians: divide by 180 and times by pi
- To convert radians to degrees: divide by pi and times by 180

## sec(x), cosec(x) and cot(x)

- sec(x) = 1/cos(x)
- cosec(x) = 1/ sin(x)
- cot(x) = 1/tan(x)

### Question 1

### Question 2

### Question 3 (Hard)

## Pythagorean Identities

- S = I + T
- sec
^{2}(x) = 1 + tan^{2}(x) - cosec
^{2}(x) = 1 + c0t^{2}(x)

### Question 4

### Question 5

### Question 6

### Question 7

## Compound Angle Identities

- sin(A+B) = sinAcosB + cosAsinB
- cos(A+B) = cosAcosB - sinAsinB
- If one sign changes e.g. + to = then all the signs change
- To derive sin(2A), work out sin(A+A) and cos(2A) would be cos(A+A)
- sin(2A) = 2sinAcosA
- cos(2A) = 1 - 2sin
^{2}A or 2cos^{2}A - 1