sin(pi/12), using difference of angles formula | Summary and Q&A

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April 22, 2017
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blackpenredpen
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sin(pi/12), using difference of angles formula

TL;DR

This video explains how to find the exact value for the sine of PI/12 (15 degrees) using the angle difference formula.

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Questions & Answers

Q: What is the angle being discussed in the video?

The video focuses on finding the exact value for the sine of PI/12, which is equivalent to 15 degrees.

Q: How is PI/12 reduced to 15 degrees?

PI/12 is reduced to 15 degrees by multiplying it by 180 degrees/PI, canceling out the radians. This simplifies the angle measurement.

Q: What formulas are used to calculate the sine of 15 degrees?

The video utilizes the angle difference formula for the sine. It expresses the sine of 15 degrees as the sine of 45 degrees times the cosine of 30 degrees, minus the cosine of 45 degrees times the sine of 30 degrees.

Q: How are special angles like 30 and 45 degrees utilized in the calculations?

Special angles like 30 and 45 degrees are used as reference points to simplify the calculations. The ratios of their sides (opposite, adjacent, hypotenuse) are utilized to determine the values for sine and cosine.

Summary & Key Takeaways

  • The video demonstrates how to find the exact value for the sine of PI/12 (15 degrees) using the angle difference formula.

  • It explains the process of reducing PI/12 to 15 degrees and simplifying it.

  • The video also shows how to use the angle difference formula to calculate the sine of 15 degrees.

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