vault backup: 2024-09-13 16:23:00
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.obsidian/app.json
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.obsidian/app.json
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"downscalePercent": 100
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"downscalePercent": 100
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},
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},
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"spellcheck": true,
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"spellcheck": true,
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"focusNewTab": false
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"focusNewTab": false,
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"alwaysUpdateLinks": true
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}
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}
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@ -4,7 +4,7 @@ The unit circle has a center a $(0, 0)$, and a radius of $1$ with no defined uni
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Sine and cosine can be used to find the coordinates of specific points on the unit circle.
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Sine and cosine can be used to find the coordinates of specific points on the unit circle.
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**Sine likes $y$, and cosine likes $x$.**
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**Sine likes $y$, and cosine likes $x$.**
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![image](./assets/sincoscirc.png)
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When sine is positive, the $y$ value is positive. When $x$ is positive, the cosine is positive.
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When sine is positive, the $y$ value is positive. When $x$ is positive, the cosine is positive.
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$$ cos(\theta) = x $$
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$$ cos(\theta) = x $$
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@ -15,7 +15,8 @@ $$ sin(\theta) = y $$
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| ------ | --- | ------------------------------- | ------------------------------ | ------------------------------ |
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| ------ | --- | ------------------------------- | ------------------------------ | ------------------------------ |
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| Cosine | 1 | $\frac{\sqrt{3}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ |
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| Cosine | 1 | $\frac{\sqrt{3}}{2}$ | $\frac{\sqrt{2}}{2}$ | $0$ |
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| Sine | 0 | $\frac{1}{2}$ | $\frac{\sqrt{2}}{2}$ | <br>$1$ |
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| Sine | 0 | $\frac{1}{2}$ | $\frac{\sqrt{2}}{2}$ | <br>$1$ |
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![image]()
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![image](./assets/unitcirc.png)
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## The Pythagorean Identity
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## The Pythagorean Identity
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The Pythagorean identity expresses the Pythagorean theorem in terms of trigonometric functions. It's a basic relation between the sine and cosine functions.
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The Pythagorean identity expresses the Pythagorean theorem in terms of trigonometric functions. It's a basic relation between the sine and cosine functions.
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education/math/MATH1060 (trig)/assets/sincoscirc.png
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