Download Trigonometric Formulas

Trigonometric Formulas – Handy Summary Sheet
1st Quadrant Measures of common angles:

0
30
45
60
90
rad
0
 /6
 /4
 /3
 /2
sin 
0
1/ 2
2 /2
3/2
1
cos 
1
3/2
2 /2
1/ 2
0
Be able to derive the values of sine and cosine for all multiples of the above angles using
symmetry on the unit circle.
Also, be able to derive the values of tangent, secant, cosecant and cotangent.
Also, be able to draw accurate graphs of the sine and cosine functions
Inverse trig functions:
y = sin-1 x: y will be in Quadrant 1 or Quadrant 4, use symmetry to get other answers.
y = cos-1 x: y will be in Quadrant 1 or Quadrant 2, use symmetry to get other answers.
y = tan-1 x: y will be in Quadrant1 or Quadrant 4, use symmetry to get other answers.
Know the domains and ranges of the inverse trig functions!!
Some Common Basic Identities (You should know these):
tan x 
sin x
cos x
sin2 x + cos2 x = 1
sec x 
 x  1  cos x
cos 2   
2
 2
1
sin x
cot x 
cos x
sin x
cos2 x = 1 - sin2 x)
cos (2x) = cos2 x - sin2 x = 2cos2 x - 1 = 1 - 2sin2 x.


cos x    sin x
2

sin(-x) = -sin(x), tan(-x) = -tan(x)
cos(-x) = cos(x)
csc x 
(Corollaries: sin2 x = 1 - cos2 x,
sin (2x) = 2 sin x cos x


sin  x    cos x
2

1
cos x
(shift identities)
(sine and tangent are odd functions)
(cosine is an even function)
 x  1  cos x
sin 2   
2
 2
(half-angle formulas)
Half-angle formulas, sum/difference formulas and product to sum formulas will be given
in the test.
Right Triangles:
sin  
opp
adj
opp
; cos  
; tan  
hyp
hyp
adj
"Soh-Cah-Toa". Remember, csc x = 1/sin x, sec x = 1/cos x, cot x = 1/tan x.
Use Pythagoras' formula to determine unknown sides in a right triangle.
Law of Cosines: (Used in SAS or SSS triangles)
Lower case a, b, c are always sides, Capital A, B, C are angles. A is opposite a, etc.
c 2  a 2  b 2  2ab cos C .
Analogous formulas for a and b.
Find the side opposite the largest given angle first, if possible. Beware of ambiguous
cases.
Law of Sines:
sin A sin B sin C


a
b
c
Make sure you're in the right mode (degree/radian).