What is the sine-on-top form of the sine rule??
$$ \frac{\sin(A)}{a} = \frac{\sin(B)}{b} + \frac{\sin(C)}{c} $$
What is the sine-on-bottom form of the sine rule??
$$ \frac{a}{\sin(A)} = \frac{b}{\sin(B)} + \frac{c}{\sin(C)} $$
Where is angle $A$ in relation to the side $a$??
Opposite.
Where is the side $c$ in relation to the angle $C$??
Opposite.
How do you draw something like “quadrilateral $ABCD$”??
Draw the quadrilateral and label the sides moving clockwise.
Why can you sometimes draw two different triangles when using the sine rule??
Because $\sin(\theta) = \sin(180 - \theta)$.
What relationship does this graph represent??
$$ \sin(\theta) = \sin(180 - \theta) $$
How do you start the proof of the sine rule??
Draw a vertical line $h$ that goes from one vertex of the triangle and intersects another at $90^{\circ}$.
If $\sin(A) = \frac{h}{b}$ and $\sin(B) = \frac{h}{a}$, then how could you turn it into the sine rule??
$$ h = b\sin(A) $$
$$ \sin(B) = \frac{(b\sin(A))}{a} $$
$$ \frac{\sin(B)}{b} = \frac{\sin(A)}{a} $$
How could you write $sin(A)$ in terms of $b$ and $h$??
$$ \sin(A) = \frac{h}{b} $$
How could you write $sin(B)$ in terms of $a$ and $h$??
$$ \sin(A) = \frac{h}{a} $$
If the sine rule has two solutions, then the two angles will be what??
- Obtuse
- Acute
Backlinks
Metadata
date: 2020-11-18 10:04
tags:
- '@?maths'
- '@?year-1'
- '@?school'
- '@?public'
title: Maths - Sine Rule