Proving Pythagorean Identities in Trigonometry

The video tutorial demonstrates how to prove the trigonometric identity that sine squared theta plus cosine squared theta equals one. It begins with an introduction to the identity and the use of a right triangle to define sine and cosine. The Pythagorean theorem is applied to establish the identity, followed by simplification steps. The tutorial also explores alternative forms of the identity involving tangent and secant. The video concludes with a call to action for viewers to share the content.

What is the result of sine squared theta plus cosine squared theta?

• 0

• Undefined

• 1

• 2

In a right triangle, what does sine theta represent?

• Opposite over Hypotenuse

• Opposite over Adjacent

• Adjacent over Hypotenuse

• Hypotenuse over Opposite

What does cosine theta represent in a right triangle?

• Hypotenuse over Opposite

• Adjacent over Hypotenuse

• Adjacent over Opposite

• Opposite over Hypotenuse

According to Pythagoras' theorem, what is the relationship between the sides of a right triangle?

• a squared plus c squared equals b squared

• a squared equals b squared plus c squared

• b squared plus c squared equals a squared

• a squared plus b squared equals c squared

How is the cosine squared theta derived from the sides of a right triangle?

• b squared over a squared

• a squared over b squared

• b squared over c squared

• c squared over a squared

What does a squared over c squared simplify to in terms of trigonometric functions?

• secant squared theta

• cosine squared theta

• sine squared theta

• tangent squared theta

What identity is derived by dividing sine squared theta plus cosine squared theta by cosine squared theta?

• tangent squared theta plus 1 equals secant squared theta

• cotangent squared theta plus 1 equals cosecant squared theta

• secant squared theta plus 1 equals tangent squared theta

• cosecant squared theta plus 1 equals cotangent squared theta

What trigonometric function is represented by sine over cosine?

• Cotangent

• Secant

• Tangent

• Cosecant

What is the result when cosine squared theta is divided by cosine squared theta?

• 1

• 0

• 2

• Undefined

What identity is formed by dividing sine squared theta plus cosine squared theta by sine squared theta?

• tangent squared theta plus 1 equals secant squared theta

• cosecant squared theta plus 1 equals cotangent squared theta

• cotangent squared theta plus 1 equals cosecant squared theta

• secant squared theta plus 1 equals tangent squared theta