Trig Functions

  • The trigonometric functions are also known as circular functions.
  •  In the trigonometric function is mainly used to communicate the angle of a triangle to the length of sides of a triangle.
  • Trigonometric function plays a vital role for learn triangles and modeling periodic function, between many other applications.
  • The most common trigonometric functions are the sine, natural cosine or cosine, and tangent.

 

TRIGONOMETRIC FUNCTIONS

 

Trigonometry function

Sin θ = opposite / hypotenuse = a/h

Cos θ = adjacent / hypotenuse = b/h

Tan  θ = opposite / adjacent = a/b

Cot θ = adjacent / opposite = b/a

Sec θ = hypotenuse / adjacent = h/b

Cosec θ = hypotenuse / opposite = h/a

Identities expressing trigonometric functions in terms of their complements

Cos t = sin(/2 – t)       sin t = cos(/2 – t)

Cot t = tan(/2 – t)       tan t = cot(/2 – t)

Cosec t = sec(/2 – t)       sec t = csc(/2 – t)

Identities of trigonometric function, Sine, cosine, secant, and cosecant have period 2 while tangent and cotangent have period.

Sin (t + 2) = sin t

Cos (t + 2) = cos t                                  

Tan (t +) = tan t

Identities for a negative angles, Sine, tangent, cotangent, and cosecant are odd functions while cosine and secant are even functions.

Sin –t = –sin t

Cos –t = cos t

Tan –t = –tan t

Sum formulas for sine and cosine

Sin (s + t) = sin s cos t + cos s sin t

Cos (s + t) = cos s cos t – sin s sin t

Double angle formulas for sine and cosine

Sin 2t = 2 sin t cos t

Cos 2t = cos2 t – sin2 t = 2 cos2 t – 1 = 1 – 2 sin2 t

Trigonometric ratios of complementary angles

1) Cos (90-θ) =sinθ

2) Tan (90-θ) =cotθ

3) Sec (90-θ) =cosecθ

4) Cot (90-θ) =tanθ

 

Relation between trigonometric ratios; solving trigonometric formulas

Trigonometric formulas:

1) Sinθ=1/cosecθ `rArr` cosecθ=1/sinθ => sinθ.cosecθ=1

2) Cosθ=1/secθ=> secθ=1/cosθ=>secθ.cosθ=1

3) Tanθ=1/cotθ=>cotθ=1/tanθ=>tanθ.cotθ=1

 

FORMULA FOR FINDING ANGLES

 

Tables for Trigonometric angle .