Trigonometric Functions and Identities

The video tutorial explains how to find the exact value of cosine of phi plus theta using the angle addition formula. It starts by introducing the angles theta and phi, and their cosine values. The tutorial then explains the angle addition formula for cosine and uses the Pythagorean identity to calculate the sine values of theta and phi. It discusses the quadrants in which theta lies to determine the sign of its sine value. Finally, the tutorial performs the calculation to find the exact value of cosine of phi plus theta.

What is the range of theta as given in the problem?

• pi/2 to 3pi/2

• pi to 2pi

• 0 to pi

• 0 to 2pi

What is the cosine of phi as provided in the problem?

• 5/13

• 1/2

• 7/25

• 3/5

Which formula is used to find the cosine of the sum of two angles?

• Angle Addition Formula

• Sine Rule

• Pythagorean Theorem

• Cosine Rule

What is the value of cosine of theta?

• 1/2

• -sqrt(3)/2

• sqrt(2)/2

• -1/2

What identity is used to find the sine of theta?

• Pythagorean Identity

• Law of Tangents

• Cosine Rule

• Sine Rule

In which quadrants does theta lie?

• Third and Fourth

• First and Fourth

• Second and Third

• First and Second

What is the sine of theta based on its quadrant?

• -sqrt(3)/2

• sqrt(3)/2

• -1/2

• 1/2

What is the sine of phi?

• 24/25

• -24/25

• 7/25

• -7/25

What is the significance of the angle phi being acute?

• It is between pi and 3pi/2

• It is between pi/2 and pi

• It is between 3pi/2 and 2pi

• It is between 0 and pi/2

What is the final expression for cosine of phi plus theta?

• 24 - 7sqrt(3)/50

• 7 + 24sqrt(3)/50

• 24 + 7sqrt(3)/50

• 7 - 24sqrt(3)/50