vangstosiis
2022-07-25
Answered

How do you find $\mathrm{tan}(20)$ using the unit circle?

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Ali Harper

Answered 2022-07-26
Author has **16** answers

What units is "20" in? First of all, ${20}^{\circ}$ is not a"standard" angle, so it would be hard to use the identity

$\mathrm{tan}(x)=\frac{\mathrm{sin}(x)}{\mathrm{cos}(x)}$, referring to the unit circles for sin and cos.

$\mathrm{tan}(x)=\frac{\mathrm{sin}(x)}{\mathrm{cos}(x)}$, referring to the unit circles for sin and cos.

Haley Madden

Answered 2022-07-27
Author has **7** answers

To use the Unit Circle, the values have to be between -1 and 1. Or, you could take the value of the $\frac{\mathrm{sin}(\theta )}{\mathrm{cos}(\theta )}$ to get the answer, for $\mathrm{tan}(\theta )$ that is.

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Is this argument valid or invalid?

Valid or Invalid

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I calculated $\mathrm{sin}75}^{\circ$ as $\frac{1}{2\sqrt{2}}+\frac{\sqrt{3}}{2\sqrt{2}}$, but the answer is $\frac{\sqrt{2}+\sqrt{6}}{4}$. What went wrong?

I calculated the exact value of $\mathrm{sin}75}^{\circ$ as follows:

${\mathrm{sin}75}^{\circ}=\mathrm{sin}({30}^{\circ}+{45}^{\circ})$

$=\mathrm{sin}30\xb0\mathrm{cos}45\xb0+\mathrm{cos}30\xb0\mathrm{sin}45\xb0$

$=\frac{1}{2}\xb7\frac{1}{\sqrt{2}}+\frac{\sqrt{3}}{2}\xb7\frac{1}{\sqrt{2}}$

$=\frac{1}{2\sqrt{2}}+\frac{\sqrt{3}}{2\sqrt{2}}$

The actual answer is

$\frac{\sqrt{2}+\sqrt{6}}{4}$