Understanding the Angle Addition Formula for Sine

The video tutorial explains the angle addition formula for sine, demonstrating that the sine of x plus y equals the sine of x times the cosine of y plus the cosine of x times the sine of y. The proof is illustrated using a diagram with right triangles, where the hypotenuse is one. The video breaks down the problem by decomposing segment DF into DE and EF, and calculating their lengths using trigonometric identities. The proof is completed by showing the equivalence of these segments to the sine of x plus y.

What is the main goal of the video tutorial?

• To prove the angle addition formula for sine

• To demonstrate the Pythagorean theorem

• To explain the concept of cosine

• To solve a quadratic equation

In the diagram, what is the hypotenuse of the red right triangle?

• The length of segment CB

• The length of segment DF

• The length of segment AC

• The length of segment DC

How is the segment DF decomposed?

• Into segments AB and BC

• Into segments DC and DF

• Into segments AC and CB

• Into segments DE and EF

What is the relationship between segment CB and the sine of y?

• CB is equal to cosine of x times cosine of y

• CB is equal to sine of x times cosine of y

• CB is equal to cosine of y times sine of x

• CB is equal to sine of y times cosine of x

What is the length of segment DC in terms of sine?

• Sine of x

• Sine of y

• Cosine of y

• Cosine of x

How is the angle y related to the angles in the triangle?

• It is equal to 90 degrees

• It is equal to the angle at the base of the triangle

• It is equal to 180 degrees

• It is equal to the angle at the top of the triangle

What is the cosine of angle y in triangle DEC?

• Segment DE over sine of x

• Segment DC over cosine of x

• Segment DE over cosine of x

• Segment DC over sine of x

What is the final expression for DE in terms of sine and cosine?

• Sine of x times cosine of y

• Cosine of x times sine of y

• Sine of y times cosine of x

• Cosine of y times sine of x

What is the sum of DE and CB equal to?

• Cosine of x minus y

• Sine of x plus y

• Cosine of x plus y

• Sine of x minus y

What is the conclusion of the proof?

• The tangent addition formula is proven

• The angle addition formula for sine is proven

• The Pythagorean theorem is proven

• The cosine rule is proven