trigonometry formulas

Identities

= 1

1 +

1 +

Trigonometry ratios

sinѲ =

cosѲ =

tanѲ =

cosecѲ =

secѲ =

cotѲ =

Relation between trigonometric ratios

SinѲ =

cosecѲ =

cosѲ=

secѲ =

tanѲ =

cotѲ =

tanѲ=

cotѲ =

Values of trigonometric ratios

 Sin Ѳ 0 1 0 cos Ѳ 1 0 -1 tan Ѳ 0 1 ∞ -1 0 cot Ѳ ∞ 1 0 -1 ∞ sec Ѳ 1 2 ∞ -2 -1 cosec Ѳ ∞ 2 1 2 ∞

1. sin(-Ѳ) = -sin Ѳ

con(-Ѳ) = cosѲ

tan(-Ѳ)=-tanѲ

2. sin (90- Ѳ) =cosѲ

cos(90 – Ѳ) = sinѲ

tan(90- Ѳ) = cotѲ

3. sin(90+ Ѳ) = cos Ѳ

cos(90+ Ѳ)=-sin Ѳ

tan(90+ Ѳ)=-cot Ѳ

4. sin(– Ѳ) = sin Ѳ

cos(– Ѳ) = -cos Ѳ

tan(– Ѳ) = -tan Ѳ

5. sin(+ Ѳ) = -sin Ѳ

cos(+ Ѳ) = -cos Ѳ

tan(+ Ѳ) = tan Ѳ

6. sin(+ Ѳ) = -cos Ѳ

cos(+ Ѳ) = sin Ѳ

tan(+ Ѳ) = -cot Ѳ

sin(A +B) =sin A cos B + cos A sin B,

sin(A -B) = sin A cos B – cos A sib B

cos (A +B) = cos A cos B –sin A sin B,

cos(A -B) = cos A cos B + sin A sin B

tan(A +B) =

tan(A -B) =

cot(A +B) =

cot(A – B) =

sin(A + B) sin (A -B) =

=

Cos(A + B) cos (A – B) =

=

2sin A cos B = sin (A +B) +sin (A – B)

2cos A Sin B = sin (A +B) – sin (A – B)

2cos A cos B= cos (A +B) + cos (A – B)

2sin A sin B = cos (A -B) – cos (A + B)

sin C + sin D = 2 sin (

sin C – sin D = -2 cos (

cos C + Cos D = 2 cos (

cos C – cos D = 2 sin (

sin2A = 2 sin A cos A

cos 2A =

=

= 1 –

sin2A =

cos2A =

tan 2A =

tan 3A =

sin 3A = 3 sin A – 4

cos 3A = 4-3 cos A

= ±(sin A +cos A)

= ±(sin A – cos A)

Or

Cosine formula

cosA =

cosB =

cosC =

Projection formula

a = b cos C + c cos B

b = c cos A + a cos C

c = a cos B + b cos A

tangent formula

tan(

tan(

tan(

sin

sin

sin

cos

cos

tan

tan

tan

Where s = (a+b+c)

sin A =

sin B =

sin C =