is there an easy way to solve sin 8pi/7 ?

[spoog74]

Anyone know of any good tricks to solve sin 8pi/7 ? The answer is something like -sinpi/7

But how would u know that?

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[PhansterZ]

Anyone know of any good tricks to solve sin 8pi/7 ? The answer is something like -sinpi/7

But how would u know that?

8 pi/7 is in the third quadrant, which means sin is negative.
to get how far it goes into the third quadrant, just take away pi.

8pi/7 - pi
= 8pi/7 - 7pi/7
= pi/7

it goes pi/7 into the third quadrant, in which sin is negative.
therefore it's -sin pi/7

 

[spoog74]

8 pi/7 is in the third quadrant, which means sin is negative.
to get how far it goes into the third quadrant, just take away pi.

8pi/7 - pi
= 8pi/7 - 7pi/7
= pi/7

it goes pi/7 into the third quadrant, in which sin is negative.
therefore it's -sin pi/7

this is probably a dumb question, but how do you know it is in the third quadrant? Are there facts i should memorize pertaining to this question?

 

[FROGGBUSTER]

Memorize and know how to apply the unit circle, it will save you time on the DAT. 👍

 

[PhansterZ]

this is probably a dumb question, but how do you know it is in the third quadrant? Are there facts i should memorize pertaining to this question?

if it helps you can convert the radians into degrees.

pi = 180 degrees.

so 8pi/7 ~ 206 degrees.
and 206 degrees is in third quadrant.

Well, you should know where the angle lies, so you can find out if the values or sin and cos are positive or negative.

In other words, you should be familiar with the unit circle.

 

[spoog74]

if it helps you can convert the radians into degrees.

pi = 180 degrees.

so 8pi/7 ~ 206 degrees.
and 206 degrees is in third quadrant.

Well, you should know where the angle lies, so you can find out if the values or sin and cos are positive or negative.

In other words, you should be familiar with the unit circle.

Thank u aLL!!