Trigonometric Identities and Formulas

The video reviews trigonometry basics, including SOH-CAH-TOA, and explores trigonometric functions like sine, cosine, and tangent. It covers Pythagorean identities, angle sum identities, and double angle identities, demonstrating their derivations. The video encourages exploring and deriving new identities, highlighting the cosine of negative angles.

What is the sine of an angle in a right triangle according to SOH-CAH-TOA?

• Adjacent over hypotenuse

• Hypotenuse over opposite

• Opposite over hypotenuse

• Adjacent over opposite

Tags

CCSS.HSF.TF.A.2

Which trigonometric function is the reciprocal of sine?

• Cotangent

• Tangent

• Cosecant

• Secant

Tags

CCSS.HSF.TF.A.2

What is the relationship between cotangent and tangent?

• Cotangent is the reciprocal of tangent

• Cotangent is the same as tangent

• Cotangent is the square of tangent

• Cotangent is the inverse of tangent

Tags

CCSS.HSF.TF.C.8

What is the Pythagorean identity involving sine and cosine?

• sine theta plus cosine theta equals 1

• sine theta times cosine theta equals 1

• sine squared theta minus cosine squared theta equals 1

• sine squared theta plus cosine squared theta equals 1

Tags

CCSS.HSF.TF.C.8

How can you derive the identity for secant squared theta?

• Multiply the Pythagorean identity by sine squared

• Divide cosine squared by sine squared

• Divide sine squared by cosine squared

• Divide the Pythagorean identity by cosine squared

Tags

CCSS.HSF.TF.C.9

What is the formula for the sine of the sum of two angles?

• cosine a times cosine b minus sine a times sine b

• sine a times sine b minus cosine a times cosine b

• sine a times cosine b plus sine b times cosine a

• sine a times sine b plus cosine a times cosine b

Tags

CCSS.HSF.TF.C.9

What is the formula for the cosine of the sum of two angles?

• cosine a times sine b plus sine a times cosine b

• cosine a times cosine b minus sine a times sine b

• sine a times sine b minus cosine a times cosine b

• sine a times cosine b plus sine b times cosine a

Tags

CCSS.HSF.TF.C.9

What is the double angle formula for sine?

• 2 sine a cosine a

• sine squared a minus cosine squared a

• 2 cosine a sine a

• sine a plus cosine a

Tags

CCSS.HSF.TF.C.9

What is the double angle formula for cosine?

• cosine squared a plus sine squared a

• cosine squared a minus sine squared a

• 2 cosine a sine a

• sine squared a minus cosine squared a

Tags

CCSS.HSF.TF.A.4

What is the cosine of a negative angle?

• Sine of the angle

• Cosine of the angle

• Negative cosine of the angle

• Negative sine of the angle

Tags

CCSS.HSF.TF.A.4