The graph of $y=\tan x$ for $0^{\circ} \leq x \leq 360^{\circ}$ is shown below.
Solve $\tan x=\tan 38^{\circ}$ when $90^{\circ} \leq x \leq 360^{\circ}$.

Answer

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Answer

$\boxed{x = 218^\circ}$

Steps

Step 1 ：Given the equation $y = \tan x$ for $0^\circ \leq x \leq 360^\circ$

Step 2 ：Solve $\tan x = \tan 38^\circ$ when $90^\circ \leq x \leq 360^\circ$

Step 3 ：Since the tangent function has a period of 180 degrees, we can add 180 degrees to 38 degrees to find another solution within the given range

Step 4 ：$x = 38^\circ + 180^\circ$

Step 5 ：$x = 218^\circ$

Step 6 ：$\boxed{x = 218^\circ}$