# How do the sum and difference formulas for sine differ from cosine?

## How do the sum and difference formulas for sine differ from cosine?

The difference formula for sines states that the sine of the difference of two angles equals the product of the sine of the first angle and cosine of the second angle minus the product of the cosine of the first angle and the sine of the second angle.

What are the sum and difference formulas for sine?

Sine and Cosine of a Sum = (cos A + i sin A) (cos B + i sin B) cos(A + B) + i sin(A + B) = (cos A cos B − sin A sin B) + i (sin A cos B + cos A sin B)

### Which formulas are used for sine and cosine?

Addition and Subtraction Formulas for Sine and Cosine

SUM AND DIFFERENCE FORMULAS FOR SINE AND COSINE
Variety of Names: For all real numbers a and b :
Addition Formula for Sine Sum Formula for Sine Sine Addition Formula Sine Sum Formula sin(a+b)=sina cosb+cosa sinb ⁡ ( a + b ) = sin ⁡ ⁡ ⁡ ⁡

What is cosine difference?

The difference formula for cosines states that the cosine of the difference of two angles equals the product of the cosines of the angles plus the product of the sines of the angles. The sum and difference formulas can be used to find the exact values of the sine, cosine, or tangent of an angle.

## What is sum and difference?

SUM – The sum is the result of adding two or more numbers. DIFFERENCE – The difference of two numbers is the result of subtracting these two numbers. QUOTIENT – The quotient of two numbers is the result of the division of these numbers.

How do you convert sine to cosine?

For example, cosθ = sin (90° – θ) means that if θ is equal to 25 degrees, then cos 25° = sin (90° – 25°) = sin 65°. This equation is a roundabout way of explaining why the graphs of sine and cosine are different by just a slide.

### What is the sum difference identity?

We can use the sum and difference formulas to identify the sum or difference of angles when the ratio of sine, cosine, or tangent is provided for each of the individual angles. To do so, we construct what is called a reference triangle to help find each component of the sum and difference formulas.

Which is the sum and difference formula for cosine?

Ptolemy’s identities, the sum and difference formulas for sine and cosine. Double angle formulas for sine and cosine. Note that there are three forms for the double angle formula for cosine. You only need to know one, but be able to derive the other two from the Pythagorean formula.

## What are the sum and difference formulas for sin?

Sine – Sum and Difference Formulas. The sum and difference formulas state that. sin ⁡ ( a + b) = sin ⁡ a cos ⁡ b + cos ⁡ a sin ⁡ b sin ⁡ ( a − b) = sin ⁡ a cos ⁡ b − cos ⁡ a sin ⁡ b. \\begin {aligned} \\sin (a+b) &= \\sin a \\cos b + \\cos a \\sin b \\\\ \\sin (a-b) &= \\sin a \\cos b – \\cos a \\sin b \\end {aligned} sin(a+b) sin(a−b) ​.

How are sum and difference formulas used in trigonometry?

The sum and difference formulas for sine can be derived in the same manner as those for cosine, and they resemble the cosine formulas. These formulas can be used to calculate the sines of sums and differences of angles. Given two angles, find the sine of the difference between the angles.

### How is the sine and cosine function defined?

The sine function is defined as the ratio between the opposite side of the angle, and the hipotenuse of this right triangle. The cosine function is defined as the ratio between the adjacent side of the angle, and the hipotenuse of this right triangle.