How do you find the terminal point on the unit

Agohofidov6 2021-12-26 Answered
How do you find the terminal point on the unit circle determined by \(\displaystyle{t}={5}\frac{\pi}{{12}}\) ?

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Expert Answer

lovagwb
Answered 2021-12-27 Author has 4238 answers
Explanation:
The arc is \(\displaystyle{t}={\frac{{{5}\pi}}{{{12}}}}\)
x-cordinate is : \(\displaystyle{x}={\cos{{\left({\frac{{{5}\pi}}{{{12}}}}\right)}}}\)
y-coordinate: \(\displaystyle{y}={\sin{{\left({\frac{{{5}\pi}}{{{12}}}}\right)}}}\)
Calculator gives \(\displaystyle{x}={\sin{{\left({\frac{{{5}\pi}}{{{12}}}}\right)}}}={\sin{{75}}}={0.97}\)
and \(\displaystyle{y}={\cos{{75}}}={0.26}\)
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jean2098
Answered 2021-12-28 Author has 3028 answers
The terminal point on the unit circle has the cosine as x-coordinated and the sine as y-coordinate.
\(\displaystyle{\left({\cos{\theta}},\ {\sin{\theta}}\right)}\)
In this case \(\displaystyle\theta={\frac{{{5}\pi}}{{{12}}}}\)
\(\displaystyle{\left({\cos{{\frac{{{5}\pi}}{{{12}}}}}},{\sin{{\frac{{{5}\pi}}{{{12}}}}}}\right)}\)
As \(\displaystyle\theta={\frac{{{5}\pi}}{{{12}}}}\) is not one of the special angles, we will use a calcutator to evaluate the cousine and the sine at \(\displaystyle\theta={\frac{{{5}\pi}}{{{12}}}}\).
\(\displaystyle{\cos{{\frac{{{5}\pi}}{{{12}}}}}}={{\cos{{75}}}^{\circ}\approx}{0.2588}\)
\(\displaystyle{\sin{{\frac{{{5}\pi}}{{{12}}}}}}={{\sin{{75}}}^{\circ}\approx}{0.9659}\)
Thus the coordinates of the terminal point at \(\displaystyle\theta={\frac{{{5}\pi}}{{{12}}}}\) are then:
\(\displaystyle{\left({\cos{{\frac{{{5}\pi}}{{{12}}}}}},{\sin{{\frac{{{5}\pi}}{{{12}}}}}}\right)}={\left({0.2588},{0.9659}\right)}\)
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nick1337
Answered 2022-01-08 Author has 9672 answers
Maybe this will help me, thanks
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