Sum and Difference Identities Calculator
MathCalculate a trigonometric function of the sum or difference of two angles using the sum and difference identities.
Result
The value of the selected trigonometric function evaluated at the combined angle.
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Odeh Ahwal0people find this calculator helpful
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Saved
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Frequently Asked Questions
What are the sum and difference identities?
They express a trig function of a combined angle (alpha+beta or alpha-beta) in terms of the individual sine and cosine values of alpha and beta separately, for example sin(a+b) = sin(a)cos(b) + cos(a)sin(b) and cos(a+b) = cos(a)cos(b) - sin(a)sin(b).
Why are these identities useful?
They let you find the exact trig value of an angle that is not a standard reference angle by breaking it into a sum or difference of two angles that are, for example finding cos(75 degrees) using 75 = 30 + 45.
How does this calculator compute the result?
It evaluates the selected function at the combined angle (alpha plus or minus beta) directly, which is mathematically identical to expanding it through the sum or difference identity formula, since both approaches always agree.
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