t=π/4
I tried to solve this problem but i dont even know where to start! i thought you had to divide the pie into 4 then put it on a number line, but when i checked my answer it was like in quadratic form can someone please help.
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$\begingroup$ Keep in mind that the circumference of the unit circle is $2\pi$, so $\pi/4$ corresponds to dividing a pie in eights. One trick I used to use in high school was whenever I saw the symbol $\pi$, instead of saying "pi", I would say "half rotation". $\endgroup$– John JoyCommented Feb 19, 2015 at 1:06
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2 Answers
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Hints:
The point $\;(x,y)\;$ is on the unit circle iff
$$\;x^2+y^2=1\;\iff \begin{cases}x=\cos t\\y=\sin t\end{cases}\;,\;\;t\in[0,2\pi)$$
So now just substitute $\;t=\frac\pi4\;$ to obtain your point (it has the same first and second entry, by the way)
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Notice that an angle of $t=\pi/4$ in standard position has a terminal side that bisects the first quadrant. Thus, finding the desired point $(x,y)$ is equivalent to finding the point in the first quadrant where $y=x$ intersects $x^2+y^2=1$.
