Trigonometric Equations – HSC Math

Whole number: n

1. if $sin\ θ=sin\ a,$ then $θ=nπ+(-1)^n\ a$
2. if $cosec\ θ=cosec\ a,$ then $θ=nπ+(-1)^n\ a$
3. if $cos\ θ=cos\ a,$ then $θ=2nπ±a$
4. if $sec\ θ=sec\ a,$ then $θ=2nπ±a$
5. if $tan\ θ=tan\ a,$ then $θ=nπ+a$
6. if $cot\ θ=cot\ a,$ then $θ=nπ+a$
7. if $sin\ θ=0,$ then $θ=nπ$
8. if $sin\ θ=1,$ then $θ=(4n+1)π/2$
9. if $sin\ θ=-1,$ then $θ=(4n-1)π/2$
10. if $cos\ θ=0,$ then $θ=(2n+1)π/2$
11. if $cos\ θ=1,$ then $θ=2nπ$
12. if $cos\ θ=-1,$ then $θ=(2n+1)π$
13. if $tan\ θ=0,$ then $θ=nπ$

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