Sin Cos Formulas

Sin Cos formulas are based on sides of the right-angled triangle. Sin and Cos are basic trigonometric functions along with tan function, in trigonometry. Sine of angle is equal to the ratio of opposite side and hypotenuse whereas cosine of an angle is equal to ratio of adjacent side and hypotenuse.

  • Sin θ = \(\frac{Opposite side}{Hypotenuse}\)
  • Cos θ = \(\frac{Adjacent Side}{Hypotenuse}\)

Sin Cos Formulas

Basic Trigonometric Identities for Sin 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

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 A/2 is in the first or second quadrants, the formula uses the positive sign.
  • If A/2 is in the third or fourth quadrants, the formula uses the negative sign

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

  • If A/2 is in the first or fourth quadrants, the formula uses the positive sign.
  • If A/2 is in the second or third quadrants, the formula uses the negative sign

Double and Triple angle formulas

  • Sin 2A = 2Sin A Cos A
  • Cos 2A = Cos2A – Sin2A = 2 Cos2 A- 1 = 1- Sin2A
  • Sin 3A = 3Sin A – 4 Sin 3A
  • Cos 3A = 4 Cos3A – 3CosA
  • \(\sin ^{4} x=(3 / 8)-(1 / 2) \cos (2 x)+(1 / 8) \cos (4 x)\)
  • \(\cos ^{4} x=(3 / 8)+(1 / 2) \cos (2 x)+(1 / 8) \cos (4 x)\)
  • 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(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) = cos A cos B cos C- cos A sin B sin C – sin A cos B sin C – sin A sin B cos C
  • 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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