Enter two angles, alpha, and beta, into the calculator to determine the values of all 6 trigonometric addition formulas.

Angle Addition Formulas

The following 6 equations are the trigonometric angle addition and subtraction formulas.

sin(alpha+beta)=sinalphacosbeta+sinbetacosalpha
sin(alpha-beta)=sinalphacosbeta-sinbetacosalpha
cos(alpha+beta)=cosalphacosbeta-sinalphasinbeta
cos(alpha-beta)=cosalphacosbeta+sinalphasinbeta
tan(alpha+beta)=(tanalpha+tanbeta)/(1-tanalphatanbeta)
tan(alpha-beta)=(tanalpha-tanbeta)/(1+tanalphatanbeta).

What are the addition formulas for sine and cosine? The 2 addition formulas for sine and cosine are as follows: sin (a+b) = sin(a)*cos(b) + sin(b)*cos(a) and cos(a+b) = cos(a)*cos(b)-sin(a)*sin(b).

Angle Addition Definition

An angle addition is a set of trigonometric formulas for calculating the trig values of the sum of two different angles, or the subtraction of two trigonometric identities.

How to calculate angle addition?

  1. First, determine the angle alpha. For this example, we will assume that alpha is 40 degrees.
  2. Next, determine the angle beta. For this problem, the angle beta is found to be 30 degrees.
  3. Next, determine the trigonometric angle addition you wish to calculate. We will determine the value of tan (a+b) for this problem
  4. Finally, use the formula from the table above to determine the value. tan (a+b) = -.153.

How to solve trig addition problems? Solving trigonometric addition problems is done through the formulas above. These are known as the angle addition identities and the angle subtraction identities or in other words the trigonometric addition and subtraction formulas.

Finding Trig Values Using Angle Addition Identities

The following problem is another example, of using the angle addition identities to determine trig values. For this problem, we will be trying to determine the value of the sine of the sum of two different angles, a, and b. The angles c and d are found to be 45 degrees and 15 degrees respectively. Next, we select the proper formula above and solve for the sine of the sum of those two numbers. sin (45) * cos (15) + sin (15) * cos (45) = .866.

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angle addition formula