COMPLETE TRIGNOMETRY FUNDAMENTAL

complete trigonometric Identities and equations for higher classes

Trigonometric identities and equations

Trigonometry laws and identities

trigonometric identities

Trig Table of Common Angles

Trig Table of Common Angles

Angle (degrees)

0

30

45

60

90

120

135

150

180

210

225

240

270

300

315

330

360 = 0

Angle (radians)

0

PI/6

PI/4

PI/3

PI/2

2/3PI

3/4PI

5/6PI

PI

7/6PI

5/4PI

4/3PI

3/2PI

5/3PI

7/4PI

11/6PI

2PI = 0 Square root of all given below terms

Sin(a)

(0/4)

(1/4)

(2/4)

(3/4)

(4/4)

(3/4)

(2/4)

(1/4)

(0/4)

-(1/4)

-(2/4)

-(3/4)

-(4/4)

-(3/4)

-(2/4)

-(1/4)

(0/4)

Cos(a)

(4/4)

(3/4)

(2/4)

(1/4)

(0/4)

-(1/4)

-(2/4)

-(3/4)

-(4/4)

-(3/4)

-(2/4)

-(1/4)

(0/4)

(1/4)

(2/4)

(3/4)

(4/4)

Tan(a)

(0/4)

(1/3)

(2/2)

(3/1)

(4/0)

-(3/1)

-(2/2)

-(1/3)

-(0/4)

(1/3)

(2/2)

(3/1)

(4/0)

-(3/1)

-(2/2)

-(1/3)

(0/4)

Those with a zero in the denominator are undefined (Not Defined) . They are included solely to demonstrate the pattern.

Basic Trigonometric Identities

Pythagorean Identities (and their variations)

From the unit circle, using the Pythagorean Theorem, we see that

x² + y² = 1

Since x = cos θ & y = sin θ, we get:

(sin θ)² + (cos θ)² = 1 or

sin² θ + cos² θ = 1

1. sin2 θ + cos2 θ = 1 (sin2 θ = 1 - cos2 θ) (cos2 θ = 1 - sin2 θ)

2. tan2 θ + 1 = sec2 θ (tan2 θ - sec2 θ = 1) (tan2 θ = sec2 θ – 1)

3. 1 + cot2 θ = csc2 θ (cot2 θ =  csc2 θ – 1) (1 =  csc2 θ - cot2 θ)

Opposite Angle Identities (aka Even/Odd Identities)

1. sin (-A) = - sin (A)                2. cos (-A) = cos (A)

Sum and Difference Identities

1.    sin(A + B) = sin(A)cos(B) + sin(B)cos(A)

2.  sin(A - B) = sin(A)cos(B) - sin(B)cos(A)

3.  cos(A + B) = cos(A)cos(B) – sin(A)sin(B)

4.  cos(A – B) = cos(A)cos(B) + sin(A)sin(B)

Cofunction Identities:  

1. sin θ = cos (90° – θ)	4. cos θ = sin (90° – θ)
2. tan θ = cot (90° – θ)	5. cot θ = tan (90° – θ)
3. sec θ = csc (90° – θ)	6. csc θ = sec (90° – θ)