SOLUTION: I need to find the exact value of sin(-71 pie/6) without using a calculator and I'm not sure what steps to follow?

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Question 918639: I need to find the exact value of sin(-71 pie/6) without using a calculator and I'm not sure what steps to follow?
Found 3 solutions by ewatrrr, Alan3354, Theo:
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
Add a positive multiple of 2pi so as sum of -71pi%2F6+%2B+n%282pi%29%286%2F6%29 is postive
sin%28-71pi%2F6+%2B+6%282pi%29%29++sin%28-71pi%2F6+%2B+72pi%2F6%29=+sin%28pi%2F6%29 = 1/2

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
PS It's the Greek letter pi, not the dessert, pie.

Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
you want to keep adding 2pi to your angle until it becomes positive.

the positive angle will be the equivalent of the negative angle.

it will have the exact same trig functions.

each time you add 2pi to your angle, it makes one complete revolution and is therefore the same equivalent angle.

it occupies the same exact position on the unit circle.

start with -71pi/6

2pi is equivalent to 12pi/6, so keep adding 12pi/6 to -71pi/6 until it becomes positive.

5 * 12pi/6 will get you 60pi/6, so add that to start and you will get a lot closer much quicker.

-71pi/6 + 60pi/6 = -11pi/6.

add 12pi/6 to that and you get 1pi/6 which is the same as pi/6.

pi/6 is equivalent to -71pi/6.

it's the same angle and occupies the same position in the unit circle.

your equivalent positive angle is pi/6.

if you don't recognize it in radians, then convert it to degrees.

convert pi/6 to degrees by multiplying it by 180/pi and you'll see that pi/6 radians is equivalent to 30 degrees.

the sine of 30 degrees is equal to 1/2, so the sine of pi/6 must also be equal to 1/2.

that's your solution.

sin(-71pi/6) = 1/2.

use your calculator to confirm if your calculator can handle it.

just enter sin(-71pi/6) and it should tell you that the sine is equal to 1/2.

it does on mine.

the following graph will confirm that the sine of -71pi/6 is the same as the sine of pi/6.

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