Do you know basic trig 1

Geometry Level 3

Find the number of integers n n such that sin ( n ) \sin(n) is an integer.

Clarification :

  • Angles are measured in radians.
1 0 4 2 3

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2 solutions

Aareyan Manzoor
Dec 31, 2015

we know that the only int values of sin(n) over real n are sin ( n ) = 1 , 0 , 1 \sin(n)=-1,0,1 for each we have n = π 2 + 2 k π , 0 + 2 k π , π 2 + 2 k π n=-\dfrac{\pi}{2}+2k\pi,\boxed{0}+2k\pi,\dfrac{\pi}{2}+2k\pi if you got tricked by thinking the question asked degrees, remember if the degree symbol is not given it means the argument is in radians.

Rishabh Jain
Dec 31, 2015

The only integral values sin(n) can take are 0,-1 and 1(since range of sin function is [-1,1]),n=0 is the only integral solution for which sin(n) is also a integer.(sin0=0∈Z)

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