Hey, everyone. This is a really specific type of problem that you may come across. Here we're asked to find the exact value of the expression sine of 10 degrees times cosine of 20 degrees plus the sine of 20 degrees times the cosine of 10 degrees. Now the first time that you see a problem like this, you may be thinking, okay, I don't know the sine of 10 degrees or the cosine of 20 degrees, nor do I know the sine of 20 degrees or the cosine of 10 degrees. So what do I do here? Well, looking at this, seeing as I have the same two angles in both of my terms and I have cosines and sines, I should notice that this looks really similar to one of my sum or difference formulas. Now here, since I have the sine times the cosine plus the sine times the cosine again, I am looking at my sine formulas here. Now here if I had a first angle a of 10 degrees and a second angle b of 20 degrees, this is really the sine of 10 degrees plus 20 degrees. Because if I were to expand this out using my sum formula right there, I would end up right back with this original expression. But what is 10 plus 20 degrees? Well, 10 degrees plus 20 degrees is 30 degrees. And the sine of 30 degrees is a trig value that I know using my unit circle. Now the sine of 30 degrees is simply equal to 1/2, and that's my final answer here. So when you see something that looks a little crazy like this, think about how you can manipulate your sum and difference formulas in order to get to a value here. Thanks for watching, and I'll see you in the next one.
Table of contents
- 0. Review of College Algebra4h 43m
- 1. Measuring Angles39m
- 2. Trigonometric Functions on Right Triangles2h 5m
- 3. Unit Circle1h 19m
- 4. Graphing Trigonometric Functions1h 19m
- 5. Inverse Trigonometric Functions and Basic Trigonometric Equations1h 41m
- 6. Trigonometric Identities and More Equations2h 34m
- 7. Non-Right Triangles1h 38m
- 8. Vectors2h 25m
- 9. Polar Equations2h 5m
- 10. Parametric Equations1h 6m
- 11. Graphing Complex Numbers1h 7m
6. Trigonometric Identities and More Equations
Sum and Difference Identities
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