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)
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 to solve trigonometric equations
What you have to know:
- The Pythagorean theorem.
Trigonometric identity
What you have to know:
- The Pythagorean theorem.
Area of a triangle
What you have to know:
- The Pythagorean theorem.
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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