Trigonometric Identities and Functions

The video tutorial explores trigonometric concepts, focusing on the properties of sine and cosine functions, particularly when dealing with negative angles. It explains how cosine is an even function and sine is an odd function, using the unit circle and right triangles. The tutorial also demonstrates how to derive various trigonometric identities using SOHCAHTOA and encourages understanding through graphical interpretation and exploration. The importance of being able to prove identities is emphasized, along with the utility of memorizing them for quick recall.

What is the cosine of a negative angle equal to?

• Negative sine of the angle

• Sine of the angle

• Negative cosine of the angle

• Cosine of the positive angle

Why is cosine considered an even function?

• Because cosine is always positive

• Because cosine of negative angles equals negative cosine of positive angles

• Because cosine of negative angles equals cosine of positive angles

• Because cosine is always negative

What is the sine of a negative angle equal to?

• Negative cosine of the angle

• Negative sine of the positive angle

• Sine of the positive angle

• Cosine of the angle

Why is sine considered an odd function?

• Because sine of negative angles equals sine of positive angles

• Because sine of negative angles equals negative sine of positive angles

• Because sine is always positive

• Because sine is always negative

What is the identity for sine of an angle plus pi/2?

• Cosine of the angle

• Negative cosine of the angle

• Sine of the angle

• Negative sine of the angle

How does the graph of sine relate to cosine?

• Sine graph is a vertical shift of cosine

• Sine graph is a reflection of cosine

• Sine graph is identical to cosine

• Sine graph is a horizontal shift of cosine

What is the identity for sine of a minus b?

• Sine of a times sine of b minus cosine of a times cosine of b

• Sine of a times cosine of b minus cosine of a times sine of b

• Cosine of a times cosine of b minus sine of a times sine of b

• Cosine of a times sine of b minus sine of a times cosine of b

What is the cosine of a minus b equal to?

• Cosine of a times cosine of b plus sine of a times sine of b

• Cosine of a times sine of b plus sine of a times cosine of b

• Sine of a times cosine of b plus cosine of a times sine of b

• Sine of a times sine of b plus cosine of a times cosine of b

What foundational concept is emphasized for understanding trigonometry?

• Law of Cosines

• Pythagorean Theorem

• SOHCAHTOA

• Law of Sines

What is encouraged to better understand trigonometric identities?

• Reading textbooks

• Using a calculator

• Graphical exploration

• Memorizing formulas