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| math:unit_circle [2021/01/13 04:23] – created epix | math:unit_circle [2021/01/24 20:52] (current) – [Using the Unit Circle for sin, cos, tan] epix | ||
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| ====== Unit Circle ====== | ====== Unit Circle ====== | ||
| The Unit Circle is a circle of radius **1**. It is useful as certain angles have memorable coordinates that are helpful for solving trig problems by hand. | The Unit Circle is a circle of radius **1**. It is useful as certain angles have memorable coordinates that are helpful for solving trig problems by hand. | ||
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| + | ===== Using the Unit Circle for sin, cos, tan ===== | ||
| + | * $\sin \theta$ is equal to the y value of the coordinate | ||
| + | * $\cos \theta$ is equal to the x value | ||
| + | * $\tan \theta$ is equal to the y value **divided** by the x value((this uses the identity $\tan \theta = \frac{\sin \theta}{\cos \theta}$)). | ||
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| + | Note that for $\tan \theta$, 90° and 270° ($\frac{\pi}{2}$ and $\frac{3\pi}{2}$ rad) are **undefined** as you cannot divide by zero((x values, or $\cos \theta$ is equal to zero in these two situations)). When calculating inverse trig functions, the solution is restricted between I and IV for $\sin$ and $\tan$, and I and II for $\cos$. | ||
