# Numbers | Maths with Lemon

Source: https://mathswithlemon.io/aa-geometry-trigonometry-Trigonometric%20equations.html


## Trigonometric Equations

"The two elements the traveler first captures in the big city are extra human architecture and furious rhythm. Geometry and anguish. " Federico Garcia Lorca


#### How the unit circle works


##### What you have to know:

- You must know all the basics about cos x, sin x and tan x properties. (If not, check this lesson)
- You must be able to rearrange formulae. (If not, check this lesson)

##### Key Points

- 1. Watch the video:
- 2. Read this presentation

#### How to solve trigonometric equations


##### What you have to know:

- The Pythagorean theorem.

##### Key Points

- 1. Watch the video:
- 2. Solving equations with cos x. Watch this video .

#### Trigonometric identity


##### What you have to know:

- The Pythagorean theorem.

##### Key Points

- 1. Watch the video:
- 2. Read this presentation

#### Area of a triangle


##### What you have to know:

- The Pythagorean theorem.

##### Key Points

- 1. Watch the video:
- 2. Read this presentation

#### Extra


##### Material and references:

- Hodder Book SL(ISBN: 9781510462359) : 18E

##### Key Points

- 1. You should be able to solve trigonometric equations graphically and analytically. 2. To solve \( \sin x = a \): let \( x_1 = \sin^{-1} a \), then \( x_2 = \pi - x_1 \), and find other solutions by adding or subtracting \( 2\pi \) from \( x_1 \) and \( x_2 \).
- 2. To solve \( \cos x = a \): let \( x_1 = \cos^{-1} a \), then \( x_2 = 2\pi - x_1 \), and find other solutions by adding or subtracting \( 2\pi \) from \( x_1 \) and \( x_2 \).
- 3. To solve \( \tan x = a \): let \( x_1 = \tan^{-1} a \), and find other solutions by adding or subtracting \( \pi \) from \( x_1 \).
- 4. You should also be able to solve trigonometric equations that lead to quadratic equations.

### IB Past Paper Problems

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