What is sum and difference identities?
The sum and difference formulas can be used to find the exact values of the sine, cosine, or tangent of an angle. The sum formula for tangent states that the tangent of the sum of two angles equals the sum of the tangents of the angles divided by 1 minus the product of the tangents of the angles.
What are the sum and difference trig identities?
Key Equations
| Sum Formula for Cosine | cos(α+β)=cosαcosβ−sinαsinβ |
|---|---|
| Sum Formula for Tangent | tan(α+β)=tanα+tanβ1−tanαtanβ |
| Difference Formula for Tangent | cos(α−β)=cosαcosβ+sinαsinβ |
| Cofunction identities | sinθ=cos(π2−θ) cosθ=sin(π2−θ) tanθ=cot(π2−θ) cotθ=tan(π2−θ) secθ=csc(π2−θ) cscθ=sec(π2−θ) |
What is a 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.
What is sum and difference example?
Key Equations
| Sum Formula for Cosine | cos(α+β)=cosαcosβ−sinαsinβ |
|---|---|
| Sum Formula for Tangent | tan(α+β)=tanα+tanβ1−tanαtanβ |
| Difference Formula for Tangent | tan(α−β)=tanα−tanβ1+tanαtanβ |
| Cofunction identities | sinθ=cos(π2−θ)cosθ=sin(π2−θ)tanθ=cot(π2−θ)cotθ=tan(π2−θ)secθ=csc(π2−θ)cscθ=sec(π2−θ) |
What is sum and differences?
What is the purpose of sum and difference identities?
The sum and difference formulas can be used to find the exact values of the sine, cosine, or tangent of an angle.
What is cos 4x equivalent to?
hey friend the formula of cos4x is. = cos(2x)cos(2x) – sin(2x)sin(2x) = cos^2(2x) – sin^2(2x) = cos^2(2x) – (1 – cos^2(2x)) = 2cos^2(2x) – 1.
What is the meaning of sum and difference?
How are sum and difference formulas used to verify identities?
Use sum and difference formulas to verify identities. Finding the exact value of the sine, cosine, or tangent of an angle is often easier if we can rewrite the given angle in terms of two angles that have known trigonometric values. We can use the special angles, which we can review in the unit circle shown in Figure 2.
How are cofunction identities used in trigonometry?
Cofunction identities are derived directly from the difference identity for cosine. The cofunction identities show the relationship between sine, cosine, tangent, cotangent, secant, and cosecant. The value of an angle’s trig function equals the value of the angle’s complement’s cofunction.
When do you use sum and difference formulas?
In this section, you will: Use sum and difference formulas for cosine. Use sum and difference formulas for sine. Use sum and difference formulas for tangent. Use sum and difference formulas for cofunctions. Use sum and difference formulas to verify identities.
Which is an example of a cofunction identity?
From these relationships, the cofunction identities are formed. ( π 2 − θ): opposite over hypotenuse. Thus, when two angles are complimentary, we can say that the sine of θ θ equals the cofunction of the complement of θ θ . Similarly, tangent and cotangent are cofunctions, and secant and cosecant are cofunctions.