Video: Simplifying Trigonometric Expressions Using Sum and Difference of Angles Identities

Simplify sin 147° cos 120° − cos 147° sin 120°.

01:36

Video Transcript

Simplify sine of 147 degrees times cosine of 120 degrees minus cosine of 147 degrees times sine of 120 degrees.

Really the only thing that needs to happen here is that we need to recognize this statement is difference of angles. And we have an identity here that can help us simplify. Sine of 𝑎 minus 𝑏 equals sin 𝑎 times cosine of 𝑏 minus cosine of 𝑎 times sine of 𝑏.

What we’re given, sine of 147 cosine of 120, we can label as sine 𝑎 times cosine of 𝑏 minus cosine of 𝑎 times sine of 𝑏. The 𝑎 values are 147 degrees and the 𝑏 values equal 120 degrees.

Our identity tells us that all of this must be equal to sine of 𝑎 minus 𝑏. And for us, that means sine of 147 minus 120. Sine of 27 degrees equals sine of 147 degrees times cosine of 120 degrees minus cosine of 147 degrees times sine of 120 degrees.

The simplified form of that expression is just sine of 27 degrees.

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