Trigonometry: Using Sum and Difference Formulas
This is a free lesson from our course in Trigonometry
 
   
In this lesson you'll learn more details of how to find the values of the sine and the cosine functions using the sum and difference formulas. It is explained by instructor with the help of a video having some examples and practice questions with solution. It is used in trigonometric applications to find the values of sine and cosine functions for which the angle measures are given in degree or in radians and also to evaluate expressions for which the angle measures of A and B are unknown. (More text below video...)
<h2>Trigonometry - Using Sum and Difference Formulas</h2> <p>Degree, sum and difference formulas, video, sum formula, difference formula, sine, cosine, angle measure, explain, Pythagorean Theorem, example, solution, sine function, cosine function, sin, cos, trigonometric identities, practice questions, quizzes</p> <p>Let us find value of sin (A + B); where sin A = 3/5, cos B = 9/41 and 0 < A, B< PI/2. You can use Pythagorean Theorem x square + y square = r square and sin A = 3/5 i.e. y/r, to get cos A = 4/5. Similarly, using the Pythagorean Theorem and cos B = 9/41 i.e. x/r, you'll get sin B = 40/41. Now substitute these values in sin(A + B) = sin A cos B + cos A sin B. You will get the answer 187/205.</p>
Other useful lessons:
Sum and Difference Formulas
Double and Half Angle Formulas
Using Double and Half Angle Formulas
(Continued from above) For example: Let us find value of sin (A + B); where sin A = 3/5, cos B = 9/41 and 0 < A, B< /2.
You can use Pythagorean Theorem x2 + y2 = r2 and sin  A = 3/5 i.e. y/r, to get cos A = 4/5.
Similarly, using the Pythagorean Theorem and cos B = 9/41 i.e. x/r, you'll get sin B = 40/41. Now substitute these values in sin (A + B) = sin A cos B + cos A sin B. You will get the answer 187/205.
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