Trigonometric Identities and Formulas

The video tutorial covers the multiplication and division of angles, focusing on using trigonometric identities such as cosine and sine half-angle and double angle identities. It provides examples and problem-solving techniques, emphasizing the importance of understanding the quadrant in which an angle lies to determine the sign of the result. The tutorial also highlights the use of these identities in calculus and other mathematical applications.

What is the result of applying the half-angle identity to cosine of 30 degrees?

• 1 plus square root of 3 over 2 all over 2

• 1 minus square root of 3 over 2 all over 2

• Square root of 2 over 2

• Square root of 3 over 2

How do you determine the sign when using a half-angle identity?

• By checking the sign of sine theta

• By checking the sign of cosine theta

• By checking the quadrant of theta over 2

• By checking the quadrant of theta

What is the cosine of 105 degrees using the half-angle identity?

• Undefined

• Negative

• Positive

• Zero

Which formula is used for sine of theta over 2?

• Square root of 1 plus cosine theta all over 2

• Square root of 1 minus cosine theta all over 2

• Square root of 1 plus sine theta all over 2

• Square root of 1 minus sine theta all over 2

What is the sine of 60 degrees using the double angle identity?

• Root 2 over 2

• 1

• 1 over 2

• Root 3 over 2

Which identity is frequently used in calculus for sine of two theta?

• Sine of two theta equals 2 sine theta cosine theta

• Sine of two theta equals sine theta cosine theta

• Sine of two theta equals 1 minus cosine squared theta

• Sine of two theta equals cosine squared theta minus sine squared theta

If cosine of theta equals 3/5, what is the tangent of 2 theta?

• 16/9

• 8/3

• 24/7

• 3/4

Which formula can be used to find cosine of two theta?

• 1 minus 2 sine squared theta

• Cosine squared theta minus sine squared theta

• All of the above

• 2 cosine squared theta minus 1

What is the result of sine squared theta equals one-half?

• Sine of theta equals plus or minus root 2 over 2

• Sine of theta equals plus or minus root 3 over 2

• Sine of theta equals plus or minus 1 over 2

• Sine of theta equals plus or minus 1 over root 2

In which quadrants does sine of theta equal plus or minus 1 over root 2?

• First and second

• Second and third

• First and third

• All quadrants