evaluate sin of 5pi/4?

sin(5π/4)

convert 5π/4 to degrees..

5π/4 x 180/π=225°

sin(225°)=-1/√(2) or -0.7071067 answer//

Do you know what the sin of pi is? You won't get the answer if you use a calculator and punch in 3.14 and hit (sin). Are you learning what radians are? This goes towards answering the question, sorry.

So 5pi/4 is "one and a quarter of pi" which is the first half of a circle and a little more. Looking at an old fashioned clock with hands, starting at 3 o'clock, going through 2, 1, 12, 11, 10, 9, and a little more, to "8" on that clock. That is the angle you are looking for, from the center of the clock to the "8". It's actually a little farther, more like between the 7 and 8.

One pi would get you to the "9" on this clock. So 5/4ths is a little more than one, as you remember from math class (5 divided by 4 = 1.25). That is how you get past the "9" on the clock.

You said "explain" so there is explain.

You are in quadrant 3.

5pi/4 *(180/pi) = 225 degrees.

Since you are in quadrant 3, the sine will be negative (so will the cosine).

At 225 degrees, the value would be the same as 45 degrees except for the minus sign.

sin(5pi/4) = - sin(pi/4)

= - (sqrt(2))/2

Looking at the symmetry of the graph of y=sin(x), we can see that sin(5pi/4) = -sin(pi/4)

Sin(pi/4) = 1/sqrt(2)

So sin(5pi/4) = -1/sqrt(2)

sin 5pi/4=sin 225=sin (270-45)=cos 45=-1/square root of 2=-.707

Perhaps its good to convert to degrees = 225 degrees

If you sketch the graph of sinx from 0 to 360

you will see that sin225 = -sin45

You can calculate sin45 from a right-angles triangle with sides 1,1 and sqrt(2).

sin ( 5pi/4 ) =sin ( pi + pi / 4 ) = sin(pi/4) = sqr(2)/2

sin (5π/4) = - sin (π/4) = - 1/√2