Understanding Trigonometric Functions for Key Angles

This video tutorial explores the sine, cosine, and tangent of the angles pi/3 and pi/6 radians, using the unit circle and 30-60-90 triangles. It begins with an introduction to these angles and their degree equivalents, followed by a demonstration of constructing an equilateral triangle. The Pythagorean theorem is applied to find side lengths, and the unit circle is used to define trigonometric functions. The video concludes with calculations of these functions for pi/6, emphasizing the importance of understanding and deriving these values.

What is the degree equivalent of pi/3 radians?

• 60 degrees

• 45 degrees

• 30 degrees

• 90 degrees

Which triangle is used to understand trigonometric functions in the unit circle?

• Isosceles triangle

• Equilateral triangle

• 30-60-90 triangle

• 45-45-90 triangle

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

• √3/2

• 1/2

• √2/2

• 1

What is the cosine of pi/3 radians?

• 1

• 1/2

• √3/2

• 0

What is the sine of pi/3 radians?

• 1

• 1/2

• 0

• √3/2

How do you calculate the tangent of an angle using sine and cosine?

• Sine divided by cosine

• Cosine divided by sine

• Sine plus cosine

• Sine minus cosine

What is the cosine of pi/6 radians?

• √3/2

• 1/2

• 0

• 1

What is the sine of pi/6 radians?

• 0

• √3/2

• 1/2

• 1

What is the tangent of pi/6 radians?

• 1

• 1/√3

• √3

• 0

How can you express 1/√3 without a radical in the denominator?

• 3/√3

• √3/3

• √3

• 1/3