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Trigonometry
“Things that I need to know”
1. SohCahToa
2. All Students Take Calculus
3. 30 ,60 ,90 ' s (1, 3, 2)
sine 
sin 
opp. side
hypotenuse
cosine 
cos 
adj. side
hypotenuse
tangent 
tan 
sin 
cos 
opp. side
adj. side
cosecant 
csc 
1
sin 
hypotenuse
opp. side
secant 
sec 
1
cos
hypotenuse
adj. side
cotangent 
cot 
1
cos 

tan  sin 
4. 45 ,45 ,90 ' s (1,1, 2 )
5. Pythagorean Theorem: a2 + b2 = c2
Pythagorean Triples:
(3,4,5)(5,12,13)(8,15,17)(7,24,25)
6. s = r  (arc length), A =
1 2
r  (area of a sector)
2
{convert  to radians!}
.
... radians
7.   180 and   31415927
8. Law of Sines:
SinX SinY SinZ
(ASA,AAS)


x
y
z
9. Law of Cosines: a2 = b2 + c2 - 2bc CosA
(SAS,SSS)
b2 = a2 + c2 - 2ac CosB
c2 = a2 + b2 - 2ab CosC
10. Trigonometric Identities: (memorize the first, solve the others)
a) sin2  + cos2  = 1
b) csc2  = 1 + cot2 
c) sec2  = 1 + tan2 
adj. side
opp. side
1
ab sin C
2
11. Area of a  =
1
bc sin A
2
or
or
1
ac sin B
2
12. Angle Addition formulas:
sin(A+B) = sinA cosB + sinB cosA
sin(A-B) = sinA cosB - sinB cosA
cos(A+B) = cosA cos B – sinA sinB
cos(A-B) = cosA cos B + sinA sinB
tan(A+B) =
tan A  tan B
1  tan A tan B
tan(A-B) =
13. Double-Angle Formulas:
sin 2 = 2 sin cos
cos 2 = cos2 - sin2
or
= 1- 2sin2
or
= 2cos2 - 1
tan 2 =
2 tan 
1  tan 2 
14. Half-Angle Formulas:
cos
sin
tan

2

2

2

1  cos
2

1  cos
2

sin 
1  cos 
1  cos 
or = sin 
15. Inverse Functions: “The fat man in his cosy secure cot”
y= Sin-1(x)  Arcsin(x) where 

y= Tan-1(x)  Arctan(x) where 
2

2
 y

 y
y= Cos-1(x)  Arccos(x) where 0  y  
2

2
tan A  tan B
1  tan A tan B