Trigonometric Identities and Properties

The video tutorial explains how to prove the sum and difference identities for sine, cosine, and tangent. It begins by constructing triangles with specific angles to align with the identities. The tutorial then calculates side lengths using trigonometric functions and derives the sine and cosine sum identities. It further extends these proofs to the tangent sum identity and demonstrates how to use these sum identities to prove the difference identities. The tutorial emphasizes the use of even and odd function properties in simplifying expressions.

What is the primary goal of the video tutorial?

• To introduce basic trigonometric functions

• To solve complex trigonometric equations

• To explore the history of trigonometry

• To prove the sum and difference identities for sine and cosine

What are the two angles used in the problem setup?

• m and n

• x and y

• p and q

• a and b

How are the two triangles arranged in the setup?

• Side by side

• One on top of the other

• In a straight line

• In a circular pattern

What is the length of the hypotenuse of the top triangle?

• y

• x

• 1

• 2

What is the sine of angle y in terms of the triangle's sides?

• Adjacent over hypotenuse

• Adjacent over opposite

• Opposite over hypotenuse

• Hypotenuse over opposite

How is the side opposite to angle y labeled?

• d

• a

• c

• b

What is the cosine of angle y in terms of the triangle's sides?

• Opposite over hypotenuse

• Adjacent over hypotenuse

• Hypotenuse over opposite

• Adjacent over opposite

What is the expression for side b in terms of sine and cosine?

• sine of x times sine of y

• sine of x times cosine of y

• cosine of x times sine of y

• cosine of x times cosine of y

What is the expression for side c in terms of sine and cosine?

• sine of x times cosine of y

• sine of x times sine of y

• cosine of x times cosine of y

• cosine of x times sine of y

What is the angle of the new triangle formed with x + y?

• y

• x

• x + y

• x - y