# 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 = $\frac{Opposite side}{Hypotenuse}$
• Cos A = $\frac{Adjacent Side}{Hypotenuse}$

## 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 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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