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Sum and Difference Trigonometric Formulas

These formulas explain how to add and subtract trigonometric functions (and their arguments). If you've got sum time, see what a difference these formulas will make for your trig toolkit.

Sine - Sum and Difference Formulas

Which of the following is equal to

\[ \sin 56 ^ \circ \cos 17 ^ \circ - \cos 56 ^ \circ \sin 17 ^ \circ ? \]

\( \sin 43 ^ \circ \cos 82 ^ \circ + \cos 43 ^ \circ \sin 82 ^ \circ = \sin N ^\circ \), where \( 0 \leq N \leq 90 \). What is the value of \(N\)?

Which of the following is equal to

\[ \sin 29 ^ \circ \cos 31 ^ \circ + \cos 29 ^ \circ \sin 31 ^ \circ ?\]

Using the Sine sum formula, what is the value of

\[ \sin 75 ^ \circ ?\]

\( \sin 21 ^ \circ \cos 37 ^ \circ + \cos 21 ^ \circ \sin 37 ^ \circ = \sin N ^\circ \), where \( 0 \leq N \leq 90 \). What is the value of \(N\)?

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