Find-the-exact-value-of-sin-if-cos-1-57-and-is-obtuse-

Question Number 33186 by NECx last updated on 12/Apr/18

F i n d t h e e x a c t v a l u e o f s i n θ i f

c o s θ = \frac{1}{57} a n d θ i s o b t u s e

Answered by MJS last updated on 12/Apr/18

\cos^{2} θ + \sin^{2} θ = 1

\sin θ = \pm \sqrt{1 - \cos^{2} θ} = \pm \sqrt{1 - \frac{1}{57^{2}}} =

= \pm \sqrt{\frac{57^{2} - 1}{57^{2}}} = \pm \frac{4 \sqrt{203}}{57} \Rightarrow

\Rightarrow θ \approx 89 ° \lor θ \approx 271 °

since both are not obtuse I guess

it should be \cos θ = - \frac{1}{57} because

then θ \approx 91 ° \lor θ \approx 269 °

and \sin θ = \frac{4 \sqrt{203}}{57}

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