Understanding Trigonometric Identities

The video tutorial explains how to determine if a trigonometric equation is not an identity by finding angles that do not satisfy the equation. It analyzes several angles, including 7π/4, 3π/2, 5π/4, and π/2, using the unit circle to calculate cosecant and cotangent values. The angle 5π/4 is identified as the one that proves the equation is not an identity, as it does not satisfy the equation.

What is the primary goal when proving a statement is not an identity?

• To find a value that makes the statement true

• To find a value that makes the statement false

• To prove the statement for all values

• To simplify the statement

What is the value of cosecant for theta equals seven pi over four?

• One

• Square root of two

• Zero

• Negative square root of two

What is the value of cotangent for theta equals seven pi over four?

• One

• Zero

• Negative one

• Square root of two

What is the result of substituting the values for theta equals seven pi over four into the equation?

• The equation is undefined

• The equation is true

• The equation is false

• The equation is zero

What is the value of cosecant for theta equals three pi over two?

• One

• Two

• Zero

• Negative one

What is the value of cotangent for theta equals three pi over two?

• One

• Two

• Negative one

• Zero

What conclusion is drawn from the substitution for theta equals five pi over four?

• The equation is zero

• The equation is undefined

• The equation is not an identity

• The equation is an identity

What is the value of cosecant for theta equals pi over two?

• Zero

• One

• Negative one

• Two

What is the value of cotangent for theta equals pi over two?

• Two

• Negative one

• One

• Zero

Which angle proves that the equation is not an identity?

• Seven pi over four

• Pi over two

• Three pi over two

• Five pi over four