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Find the exact value of s in the given interval that has the given circular function value.

Find the exact value of s in the given interval that has the given circular function-example-1
User Skybobbi
by
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1 Answer

22 votes
22 votes

Recall that:


\tan x=(\sin x)/(\cos x)\text{.}

Therefore:


\tan s=1\Leftrightarrow(\sin s)/(\cos s)=1.

Then:


\sin s=\cos s\text{.}

Now, notice that:


\sin s-\cos s=-√(2)\cos (s+(\pi)/(4)).

Then:


-\sqrt[]{2}\cos (s+(\pi)/(4))=0.

Therefore:


\cos (s+(\pi)/(4))=0.

Then:


\begin{gathered} s+(\pi)/(4)=(\pi)/(2)+n\pi, \\ s+(\pi)/(4)=(3\pi)/(2)+n\pi\text{.} \end{gathered}

Therefore:


\begin{gathered} s=(\pi)/(4)+n\pi, \\ s=(5\pi)/(4)+n\pi\text{.} \end{gathered}

Since:


s\in\lbrack\pi,(3\pi)/(2)\rbrack^{},

we get that:


s=(5\pi)/(4)\text{.}

Answer:


s=(5\pi)/(4)\text{.}

User Zrvan
by
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