Sin Cos Formulas

Sin and Cos are basic trigonometric functions which tell about the shape of a right triangle, so the Sin Cos formulas are the basic ones in trigonometry.

  • Sin A = \(\frac{Perpendicular}{Hypotenuse}\)
  • Cos A = \(\frac{Base}{Hypotenuse}\)

Sin Cos Formulas

Basic Trigonometric Identities for Sine and Cos

These formulas help in giving a name to each side of the right triangle and these are also used in trigonometric formulas for class 11. Let’s learn the basic sin and cos formulas.

  • cos2(A) + sin2(A) = 1

If A + B = 180° then:

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

If A + B = 90° then:

  • sin(A) = cos(B)
  • cos(A) = sin(B)

Sine and Cosine Formulas

To get help in solving trigonometric functions , you need to know the trigonometry formulas.

Half-angle formulas

Sin \(\frac{A}{2}\) = \(\pm \sqrt{\frac{1- Cos A}{2}}\)

  • If \(\frac{A}{2}\) lies in quadrant I or II.
  • If \(\frac{A}{2}\) lies in quadrant III or IV.

Cos \(\frac{A}{2}\) = \(\pm \sqrt{\frac{1+ Cos A}{2}}\)

  • If \(\frac{A}{2}\) lies in quadrant I or IV.
  • If \(\frac{A}{2}\) lies in quadrant II or III.

Double and Triple angle formulas

  • Sin 2A = 2Sin A Cos A
  • Cos 2A = Cos2A – Sin2A = 2 Cos2 – 1 = 1- Sin2A
  • Sin 3A = 3Sin A – 4 Sin 3A
  • Cos 3A = 4 Cos3A – 3CosA
  • Sin4A = 4 Cos3A . Sin A – 4Cos A. Sin 3A
  • Cos4 A = Cos4A – 6Cos2A.Sin2A +Sin4A
  • Sin2A = \(\frac{1 – Cos(2A)}{2}\)
  • Cos2A =\(\frac{1 + Cos(2A)}{2}\)

Sum and Difference of Angles

  • sin(A + B) = sin(A).cos(B) + cos(A)sin(B)
  • sin(B)sin(A−B)=sin(A)⋅cos(B)−cos(A)⋅sin(B)
  • cos(A+B)=cos(A)⋅cos(B)−sin(A)⋅sin(B)
  • cos(A−B)=cos(A)⋅cos(B)+sin(A)⋅sin(B)
  • sin(A+B+C)=sinA⋅cosB⋅cosC+cosA⋅sinB⋅cosC+cosA⋅cosB⋅sinC−sinA⋅sinB⋅sinC
  • cos(A+B+C)=cosA⋅cosB⋅cosC−sinA⋅sinB⋅cosC−sinA⋅cosB⋅sinC−sinA⋅cosB⋅sinC−cosA⋅sinB⋅sinC
  • Sin A + Sin B = 2Sin\(\frac{(A+B)}{2}\)Cos\(\frac{(A-B)}{2}\)
  • Sin A – Sin B = 2Sin\(\frac{(A-B)}{2}\)Cos\(\frac{(A+B)}{2}\)
  • Cos A + Cos B = 2Cos\(\frac{(A+B)}{2}\)Cos\(\frac{(A-B)}{2}\)
  • Cos A + Cos B = -2Sin\(\frac{(A+B)}{2}\)Sin\(\frac{(A-B)}{2}\)

Explore more trigonometric formulas and applications on BYJU’S. Register yourself for the same on BYJU’S.


Practise This Question

Six charges, three positive and three negative of equal magnitude are to be placed at the vertices of a regular hexagon such that the electric field at O is double the electric field when only one positive charge of same magnitude is placed at R. Which of the following arrangements of charges is possible for P, Q, R, S, T and U respectively