Trigonometric Functions and Ratios

This video tutorial introduces the basics of trigonometry, focusing on right triangles. It covers the historical context of trigonometry, explaining its Greek origins and its application in astronomy. The tutorial then delves into the properties of right triangles, defining terms like hypotenuse, opposite, and adjacent sides. It introduces the primary trigonometric ratios: sine, cosine, and tangent, and their inverses: cosecant, secant, and cotangent. The video concludes with example problems to illustrate the application of these concepts.

What is the origin of the word 'trigonometry'?

• Sanskrit

• Latin

• Greek

• Arabic

In a right triangle, what is the side opposite the right angle called?

• Opposite

• Hypotenuse

• Base

• Adjacent

Which trigonometric ratio is defined as the opposite side over the hypotenuse?

• Cosine

• Tangent

• Secant

• Sine

What is the reciprocal of the sine function?

• Cosecant

• Tangent

• Cotangent

• Secant

If the cosine of an angle is the adjacent side over the hypotenuse, what is the secant of the angle?

• Adjacent over opposite

• Hypotenuse over adjacent

• Hypotenuse over opposite

• Opposite over hypotenuse

In the example problem, if side AB is 10 and side BC is 8, what is the sine of angle A?

• 5/4

• 5/3

• 3/5

• 4/5

In the example problem, what is the cosine of angle A if side AC is 6?

• 3/5

• 4/5

• 5/3

• 5/4

What is the tangent of angle A in the example problem?

• 3/4

• 4/3

• 5/3

• 3/5

If a triangle has sides 13, 12, and 5, what is the sine of the angle opposite the side of length 5?

• 12/5

• 5/12

• 12/13

• 5/13

In the same triangle, what is the cosine of the angle opposite the side of length 5?

• 12/13

• 5/13

• 5/12

• 12/5