Exploring Trigonometric Functions through Right Triangles

The video tutorial introduces trigonometric functions, focusing on their application in right triangles. It explains the basic functions: sine, cosine, and tangent, and their reciprocal functions: cosecant, secant, and cotangent. The tutorial covers special triangles, 45-45-90 and 30-60-90, detailing how to calculate trigonometric functions for these angles. It also demonstrates using the Pythagorean theorem to find missing sides and evaluate trigonometric functions in a general triangle example.

What is the longest side of a right triangle called?

• Base

• Hypotenuse

• Adjacent

• Opposite

Which side is opposite to angle theta in a right triangle?

• Adjacent

• Hypotenuse

• Base

• Opposite

What does the sine function represent in a right triangle?

• Adjacent over Hypotenuse

• Opposite over Adjacent

• Opposite over Hypotenuse

• Hypotenuse over Opposite

What is the ratio for the tangent function?

• Hypotenuse over Adjacent

• Opposite over Hypotenuse

• Adjacent over Hypotenuse

• Opposite over Adjacent

Which trigonometric function is the reciprocal of sine?

• Cosecant

• Cotangent

• Secant

• Cosine

In a 45-45-90 triangle, what is the length of the hypotenuse if each leg is 1?

• 1

• √2

• √3

• 2

What is the cosine of 45 degrees?

• 1/√2

• √2/2

• 1

• √3/2

In a 30-60-90 triangle, what is the length of the hypotenuse if the shortest side is 1?

• √2

• 2

• 1

• √3

What is the sine of 30 degrees?

• √3/3

• 1/√2

• √3/2

• 1/2

If a right triangle has sides of lengths 5 and 12, what is the length of the hypotenuse?

• 15

• 17

• 13

• 10