The unit circle is a circle with radius 1 centered at the origin (0,0).
On the unit circle:
Remember that any point on the unit circle can be written as $(\cos \theta, \sin \theta)$ because the radius is always 1!
Depending on which quadrant $\theta$ is in, the values of $\sin \theta, \cos \theta, \tan \theta $ may change sign.
Some students use the mnemonic "All Students Take Calculus" for which trigonometric functions are positive in which quadrants.
The sine rule states: $\frac{a}{\sin A} = \frac{b}{\sin B} = \frac{c}{\sin C}$
When using the sine rule to solve for an angle, we sometimes get two possible solutions. This is called the ambiguous case.
If we know:
When solving for angle B, we get: $\sin B = \frac{7 \sin 40°}{8}$
This could give us two angles:
Both are valid solutions unless we have additional information!
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