How do I find the value of sin 5pi / 6?

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How do I find the value of sin 5pi / 6?

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Answer 1 · 2015-08-08T02:29:15

sin $\frac{5 π}{6}$ $(5pi)/6$ = $\frac{1}{2}$ $1/2$

Explanation:

Sin $\frac{5 π}{6}$ $(5pi)/6$ = sin $(π - \frac{π}{6})$ $(pi- pi/6)$ = sin $\frac{π}{6}$ $pi/6$ = sin 30 = $\frac{1}{2}$ $1/2$

Another way to think about it is to draw the angle in a Unit circle and create the "new" triangle in Quadrant II. teachtogether

Drop a perpendicular to the x-axis and you will have the correct triangle to use.
![https://www.google.com/imgres?imgurl=http%3A%2F%2Fcat.ocw.uci.edu%2Fmedia%2FOC08%2F11133%2FOC0111133_Trig2006.gif&imgrefurl=http%3A%2F%2Fcat.ocw.uci.edu%2Foo%2FgetOCWPage.php%3Fcourse%3DOC0811133%26lesson%3D2%26topic%3D2%26page%3D10&docid=AMHSUt2Ajj-ALM&tbnid=9MMwqPn6rIyQHM%3A&vet=1&w=350&h=350&safe=active&bih=560&biw=1096&ved=0ahUKEwjYmJyoiePQAhUaOsAKHebwAuAQMwghKAYwBg&iact=mrc&uact=8]
( useruploads.socratic.org )

From this triangle, you need the opposite leg length, which is $\frac{1}{2}$ $1/2$ .
Since the hypotenuse is equal to 1 in the Unit circle, the opposite leg length is the answer for sine. (dividing by 1 is not necessary)

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How do I find the value of sin 5pi / 6?

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