Trigonometry cheat sheet

its mathematics subject

1. Symbolab Trigonometry Cheat Sheet
Basic Identities:
 tan(�)=
sin(??????)
cos(??????)

 tan(�)=
1
cot(??????)

 cot(�)=
1
tan(??????)

 cot(�)=
cos(??????)
sin(??????)

 sec(�)=
1
cos(??????)

 csc(�)=
1
sin(??????)
Pythagorean Identities
 cos
2
(�)+sin
2
(�)=1
 sec
2
(�)−tan
2
(�)=1
 csc
2
(�)−cot
2
(�)=1
Double Angle Identities
 sin(2�)=2sin(�)cos(�)
 cos(2�)=1−2sin
2
(�)
 cos(2�)=2cos
2
(�)−1
 cos(2�)=cos
2
(�)−sin
2
(�)
 tan(2�)=
2tan(??????)
1−tan
2(??????)

Sum Difference Identities
 sin(�+�)=sin(�)cos(�)+cos(�)sin(�)
 sin(�−�)=sin(�)cos(�)−cos(�)sin(�)
 cos(�+�)=cos(�)cos(�)−sin(�)sin(�)
 cos(�−�)=cos(�)cos(�)+sin(�)sin(�)
 tan(�+�)=
tan(�)+tan(�)
1−tan(�)tan(�)

 tan(�−�)=
tan(�)−tan(�)
1+tan(�)tan(�)

Product To Sum Identities
 cos(�)cos(�)=
cos(�−�)+cos(�+�)
2

 sin(�)sin(�)=
cos(�−�)−cos(�+�)
2

 sin(�)cos(�)=
sin(�+�)+sin(�−�)
2

 cos(�)sin(�)=
sin(�+�)−sin(�−�)
2

Triple Angle Identities
 sin(3�)=−sin
3
(�)+3cos
2
(�)sin(�)
 sin(3�)=−4sin
3
(�)+3sin(�)
 cos(3�)=cos
3
(�)−3sin
2
(�)cos(�)
 cos(3�)=4cos
3
(�)−3cos(�)
 tan(3�)=
3tan(??????)−tan
3
(??????)
1−3tan
2(??????)

 cot(3�)=
3cot(??????)−cot
3
(??????)
1−3cot
2(??????)

2. Function Ranges:
sin(�) −1≤�≤1 arcsin(�)
−
??????
2
≤�≤
??????
2

cos(�) −1≤�≤1 arccos(�) 0≤�≤??????
tan(&#3627408485;) ∞<&#3627408486;<∞ arctan(&#3627408485;)
−
??????
2
<&#3627408486;<
??????
2

cot(&#3627408485;) ∞<&#3627408486;<∞ arccot(&#3627408485;) 0<&#3627408486;<??????
csc(&#3627408485;) −∞<&#3627408486;≤1
∪1≤&#3627408486;<∞
arccsc(&#3627408485;)
0≤&#3627408486;<
??????
2
∪??????≤&#3627408486;<
3??????
2

sec(&#3627408485;) −∞<&#3627408486;≤1∪
1≤&#3627408486;<∞
arcsec(&#3627408485;)
−??????<&#3627408486;≤−
??????
2
∪0<&#3627408486;<
??????
2

Function Values:
&#3627408428;??????&#3627408423;(??????) ??????&#3627408424;&#3627408428;(??????) &#3627408429;??????&#3627408423;(??????) ??????&#3627408424;&#3627408429;(??????)
&#3627409358; 0 1 0 Undefined
??????
&#3627409364;

1
2

√3
2

1
√3

√3
??????
&#3627409362;

1
√2

1
√2

1 1
??????
&#3627409361;

√3
2

1
√3

√3
1
√3

??????
&#3627409360;

1 0 Undefined 0
&#3627409360;??????
&#3627409361;

√3
2

−
1
2

−√3
−
1
√3

&#3627409361;??????
&#3627409362;

1
√2
−
1
√2
−
1
√3

−√3
&#3627409363;??????
&#3627409364;

1
2

−
√3
2

−1 −1
?????? 0 −1 0 Undefined
&#3627409365;??????
&#3627409364;
−
1
2

−
√3
2


&#3627409363;??????
&#3627409362;
−
1
√2
−
1
√2


&#3627409362;??????
&#3627409361;

−
√3
2

−
1
2


&#3627409361;??????
&#3627409360;

−1 0
&#3627409363;??????
&#3627409361;
−
√3
2

1
2


&#3627409365;??????
&#3627409362;
−
1
√2

1
√2


&#3627409359;&#3627409359;??????
&#3627409364;
−
1
2

√3
2