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how does sin(-13pi/4) = -5pi/4


we were asked to find the exact value of sin(-13pi/4)

how does sin(-13pi/4) = -5pi/4


we were asked to find the exact value of sin(-13pi/4)

Verified Answer :

NOTE: My solution here has +13pi/4 instead of yours as -13pi/4, however, if you just examine this solution, it could help you solve the problem yourself.


13π / 4 needs to be 'reduced' so that we find out where on the Unit Circle you are. 


To do this, subtract out 8π / 4 (2π, or a whole Unit Circle) until you can't do it anymore without getting a negative number. 


Subtracting out 8π/4 gives you 5π/4. 


Sin 5π/4 = -√2 / 2 


The reason I chose 8π/4 was because your fraction had 4 in the denominator. If it had, say, 12 in the denominator, the subtraction would have been 24π/12 (still giving 2π, or a whole Unit Circle). Make sense?

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