Trigonometric Identities and Calculations

The video tutorial walks through solving a math problem involving trigonometric identities. The instructor simplifies an equation using the identity sine squared plus cosine squared equals one, and then calculates the result using a calculator. The final result is a distance of 5.33 miles, with a brief discussion on the implications of the solution. The tutorial emphasizes the importance of simplification to reduce errors in calculations.

What trigonometric identity is used to simplify the expression involving sine and cosine?

• Sine minus cosine equals zero

• Sine squared plus cosine squared equals zero

• Sine squared plus cosine squared equals one

• Sine plus cosine equals one

What is the purpose of changing colors during the explanation?

• To correct a previous mistake

• To indicate a change in topic

• To highlight important steps

• To make the video more colorful

What is the initial expression given in the problem?

• 25 times sine squared of 15 plus cosine squared of 15

• 25 times sine of 30 plus cosine of 30

• 25 times sine of 15 plus cosine of 15

• 25 times sine squared of 30 plus cosine squared of 30

What is the simplified expression for m squared after using the trigonometric identity?

• 125 plus 100 minus 100 cosine of 15 degrees

• 25 plus 100 minus 100 cosine of 15 degrees

• 25 plus 100 minus 100 sine of 15 degrees

• 125 minus 100 plus 100 sine of 15 degrees

What does the variable m represent in the context of this problem?

• The distance traveled

• The angle in degrees

• The speed of travel

• A variable with no specific relevance

What is the value of cosine of 15 degrees used in the calculation?

• 0.86603

• 0.96593

• 0.5

• 0.70711

What is the result of 125 minus 100 times the cosine of 15 degrees?

• 28.407

• 100.593

• 125.407

• 96.593

What is the final value of m after taking the square root of the simplified expression?

• 5.43

• 5.23

• 5.53

• 5.33

What is the significance of the extra 0.33 miles mentioned at the end?

• It represents the total distance traveled

• It is the additional distance due to a wrong direction

• It is the distance to the starting point

• It is the distance covered in one hour

Why is a calculator used in the final steps of the problem?

• To verify the trigonometric identity

• To calculate the exact value of cosine

• To find the square root of the final result

• To simplify the expression further