Confusing math Questions Sin(5pi/3) = ???? I hate these so much

[Toothguy80]

Ok, so in the last test in Kaplan, it has this question for #21 and it says that

Sin 5pi/3 = ??

I thought it would be cos 2pi/3 but it's cos 5pi/3

Why? How am I supposed to solve these quickly on the test?
tell me a quick and easy strategy...

DAT math questions are very easy, I have developed many good strategies for solving these..this question remains a mystery..

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[Streetwolf]

Ok, so in the last test in Kaplan, it has this question for #21 and it says that

Sin 5pi/3 = ??

I thought it would be cos 2pi/3 but it's cos 5pi/3

Why? How am I supposed to solve these quickly on the test?
tell me a quick and easy strategy...

DAT math questions are very easy, I have developed many good strategies for solving these..this question remains a mystery..

sin 5pi/3 = cos 5pi/6 ....

 

[Toothguy80]

can u please explain?
I already know the answer

I just need to know the way to do it, so I will always get these questions right.

 

[Streetwolf]

You wrote cos 5pi/3.


Because sin pi/3 = cos pi/6 and sin pi/6 = cos pi/3.

Since the non-reducible thirds and sixths are identical (pi/6, 5pi/6, 7pi/6, 11pi/6 and pi/3, 2pi/3, 4pi/3, 5pi/3) except for sign, any sin (fraction involving thirds) will possibly equal any cos (fraction involving sixths) and vice versa. It's just a matter of determining which sign you are looking for.

Since sin (5pi/3) is in the fourth quadrant, the y coordinate is negative. With sin and thirds, we are dealing with -sqrt(3)/2. This is cos and sixths. We need to know where this happens. It happens in the second or third quadrant. So this is either cos (5pi/6) or cos(7pi/6). Both work.

 

[KEC029]

You wrote cos 5pi/3.


Because sin pi/3 = cos pi/6 and sin pi/6 = cos pi/3.

Since the non-reducible thirds and sixths are identical (pi/6, 5pi/6, 7pi/6, 11pi/6 and pi/3, 2pi/3, 4pi/3, 5pi/3) except for sign, any sin (fraction involving thirds) will possibly equal any cos (fraction involving sixths) and vice versa. It's just a matter of determining which sign you are looking for.

Since sin (5pi/3) is in the fourth quadrant, the y coordinate is negative. With sin and thirds, we are dealing with -sqrt(3)/2. This is cos and sixths. We need to know where this happens. It happens in the second or third quadrant. So this is either cos (5pi/6) or cos(7pi/6). Both work.

this must be a correct way to solve it.

but i just draw them. sin and cos waves. and match the x-axis.