Exploring Trigonometric Ratios: Sine, Cosine, Tangent, and More

Mr. Allen introduces trigonometric ratios and demonstrates how to find all six ratios for triangles using Pythagorean triples. He explains the process of calculating sine, cosine, tangent, and their reciprocals. The video also covers the necessity of rationalizing denominators, despite the speaker's personal dislike for the rule. The tutorial concludes with a summary of the calculations and a call to reconsider the rationalization rule.

What is the Pythagorean triple used in the first example?

• 3, 4, 5

• 5, 12, 13

• 8, 15, 17

• 7, 24, 25

What is the sine ratio for the first example?

• 17/8

• 8/15

• 15/17

• 8/17

What is the cosine ratio for the first example?

• 15/17

• 17/8

• 8/17

• 8/15

What is the tangent ratio for the first example?

• 15/17

• 15/8

• 8/15

• 17/15

What is the secant ratio for the first example?

• 8/17

• 17/8

• 17/15

• 15/17

What is the missing side length in the second example?

• 5

• √34

• 4

• 3

What is the sine ratio for the second example before rationalization?

• 3/√34

• √34/3

• 3/5

• 5/√34

What is the cosine ratio for the second example after rationalization?

• 5√34/34

• √34/5

• 5/√34

• 5/34

What is the tangent ratio for the second example?

• 3/5

• 3/√34

• 5/3

• √34/3

What is the cotangent ratio for the second example?

• 5/√34

• √34/5

• 5/3

• 3/5