Trigonometric Functions and Identities

Mr. Kelly introduces the Pythagorean identity, explaining its significance in trigonometry. The video covers the sine, cosine, and tangent ratios, and demonstrates how to prove the Pythagorean identity. Students learn to solve trigonometric equations using this identity and explore the relationships between tangent, sine, and cosine. The lesson concludes with practice problems and a summary of key concepts.

What is the Pythagorean Identity in trigonometry?

• sine squared plus cosine squared equals one

• sine plus cosine equals one

• sine times cosine equals one

• sine squared minus cosine squared equals one

In a unit circle, what is the length of the hypotenuse?

• √2

• 1

• 2

• 0.5

Which trigonometric function is positive in the second quadrant?

• Secant

• Tangent

• Cosine

• Sine

How is the Pythagorean Identity derived from the Pythagorean Theorem?

• By assuming the hypotenuse is 2

• By using the sine and cosine definitions

• By substituting the radius as 1

• By using the tangent function

What is the cosine of an angle if the sine is 3/5 in the second quadrant?

• 4/5

• -3/5

• -4/5

• 3/5

What is the relationship between tangent, sine, and cosine?

• Tangent equals sine times cosine

• Tangent equals sine over cosine

• Tangent equals cosine over sine

• Tangent equals sine plus cosine

If the sine of an angle is -1/4 in the third quadrant, what is the tangent?

• -√15/15

• √15/15

• -1/√15

• 1/√15