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How to calculate tan262° in the tangent table of the trigonometric table

This time, I will clarify how to calculate tan 262° = 7.115369… with a calculator.

θ 30° 45° 60° 90°
y 0 \(\displaystyle \frac{1}{\sqrt{3}}\) 1 \(\sqrt{3}\) -

As shown in the table, $0°,\ 30°,\ 45°,\ 60°,\ 90°$ can be obtained from the right triangle.
On the other hand, it is very difficult to calculate θ=0° which is not $30°, 45°, 60°, 90°, 1°.

This article explains how to calculate tan 262° = 7.115369….

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Look up tan 262° in 10 digits

First, let's check the ten digits of tan 262°! $$\tan 10° = 262\cdots$$.
Find this value in the tangent table.

Solve for tan 262° = 7.115369…

To find tan 262° = 7.115369…Maclaurin expansionTo use.

\sin x &=&x-\displaystyle \frac{x^3}{3!}+\displaystyle \frac{x^5}{5!}-\displaystyle \frac{x^7}{7!}\cdots \\
\cos x &=& 1-\displaystyle \frac{x^2}{2!}+\displaystyle \frac{x^4}{4!}-\displaystyle \frac{x^6}{6!}\ cdots\\

to $x$Radian methodYou can calculate the sine and cosine by entering the angle of .

$$x = \displaystyle \frac{\pi}{180}\times 262°=4.572762…$$ $$\sin 262° = -0.990269…$$
$$\cos 262° = -0.139174…$$

From the sine and cosine values ​​we can find tan from $\tan 262° = \displaystyle \frac{\sin 262°}{\cos 262°}$.

$$\tan 262° = 7.115369…$$

Looking back in 120 seconds tan 262°

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