Find three values theta, other than 15 degrees, such that sin theta=sin 15 degrees

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embizze eNotes educator| Certified Educator

Find three values of theta such that `sin theta=sin 15^@ ` :

One way is to realize that the period of the sine function is 360 degrees; so any `theta=15+360n,n in ZZ ` will work. (read: theta is 15 + 360n where n is an integer.)

So some possible values are ` theta=375^@,735^@,1095^@,-345^@ ` etc...

Also, if theta works, 180-theta works as well. So we could include `theta=165^@+360n ` such as 165,475,etc...