Trigonometry Cheat Sheet
tan(x)=sin(x)cos(x)
tan(x)=1cot(x)
cot(x)=1tan(x)
cot(x)=cos(x)sin(x)
sec(x)=1cos(x)
csc(x)=1sin(x)
cos2(x)+sin2(x)=1
sec2(x)−tan2(x)=1
csc2(x)−cot2(x)=1
sin(2x)=2sin(x)cos(x)
cos(2x)=1−2sin2(x)
cos(2x)=2cos2(x)−1
cos(2x)=cos2(x)−sin2(x)
tan(2x)=2tan(x)1−tan2(x)
sin(s+t)=sin(s)cos(t)+cos(s)sin(t)
sin(s−t)=sin(s)cos(t)−cos(s)sin(t)
cos(s+t)=cos(s)cos(t)−sin(s)sin(t)
cos(s−t)=cos(s)cos(t)+sin(s)sin(t)
tan(s+t)=tan(s)+tan(t)1−tan(s)tan(t)
tan(s−t)=tan(s)−tan(t)1+tan(s)tan(t)
cos(s)cos(t)=cos(s−t)+cos(s+t)2
sin(s)sin(t)=cos(s−t)−cos(s+t)2
sin(s)cos(t)=sin(s+t)+sin(s−t)2
cos(s)sin(t)=sin(s+t)−sin(s−t)2
sin(3x)=−sin3(x)+3cos2(x)sin(x)
sin(3x)=−4sin3(x)+3sin(x)
cos(3x)=cos3(x)−3sin2(x)cos(x)
cos(3x)=4cos3(x)−3cos(x)
tan(3x)=3tan(x)−tan3(x)1−3tan2(x)
cot(3x)=3cot(x)−cot3(x)1−3cot2(x)
y=sin(x)
−1≤y≤1
y=cos(x)
−1≤y≤1
y=tan(x)
−∞<y<∞
y=cot(x)
−∞<y<∞
y=csc(x)
−∞<y≤−1 ∪ 1≤y<∞
y=sec(y)
−∞<y≤−1 ∪ 1≤y<∞
y=arcsin(x)
−π 2 ≤y≤ π 2
y=arccos(x)
0 ≤ y ≤ π
y=arctan(x)
−π 2 < y<π 2 :
y=arccot(x)
0<x<π
y=arccsc(x)
0≤y<π2 ∪ π≤y<3π2
y=arcsec(x)
−π<y≤−π2 ∪ 0<y<π2 <∞
sin(x)
cos(x)
tan(x)
cot(x)
0
0
1
0
Undefined
π6
12
√32
√33
√3
π4
√22
√22
1
1
π3
√32
12
√3
√33
π2
1
0
Undefined
0
2π3
√32
−12
−√3
−√33
3π4
√22
−√22
−1
−1
5π6
12
−√32
−√33
−√3
π
0
−1
0
Undefined
7π6
−12
−√32
√33
√3
5π4
−√22
−√22
1
1
4π3
−√32
−12
√3
√33
3π2
−1
0
Undefined
0
5π3
−√32
12
−√3
−√33
7π4
−√22
√22
−1
−1
11π6
−12
√32
−√33
−√3
2π
0
1
0
Undefined