Trigonometric Functions and Identities

The video tutorial explains how to verify that triangle ABC is a right triangle using the Pythagorean theorem. It then explores how to calculate the cosine of angle ABC plus 60 degrees using trigonometric identities. The tutorial covers the evaluation of cosine and sine for specific angles and demonstrates the simplification of the resulting expression.

What theorem is used to verify that triangle ABC is a right triangle?

• Cosine rule

• Tangent rule

• Pythagorean theorem

• Sine rule

What is the problem asking to find in relation to angle ABC?

• Secant of angle ABC

• Tangent of angle ABC

• Cosine of angle ABC plus 60 degrees

• Sine of angle ABC

Which trigonometric identity is used to express the cosine of angle ABC plus 60 degrees?

• Cosine subtraction formula

• Sine addition formula

• Cosine addition formula

• Tangent addition formula

How is the cosine of angle ABC calculated?

• Opposite over hypotenuse

• Adjacent over hypotenuse

• Hypotenuse over adjacent

• Opposite over adjacent

What is the value of cosine of angle ABC?

• 8/15

• 8/17

• 17/15

• 15/17

What is the cosine of 60 degrees in a 30-60-90 triangle?

• √3/2

• 0

• 1/2

• 1

What is the sine of angle ABC?

• 15/8

• 15/17

• 17/8

• 8/17

What is the sine of 60 degrees?

• 1

• 1/2

• 0

• √3/2

What is the final expression for the cosine of angle ABC plus 60 degrees?

• 8/34 - 4√3/17

• 8/34 + 4√3/17

• 15/34 - 4√3/17

• 15/34 + 4√3/17

What is the common denominator used in the final expression?

• 17

• 34

• 51

• 68