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\(\frac{(A-B)}{2}\)

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