Understanding Trigonometry with Special Triangles

The video tutorial introduces trigonometry by emphasizing the inefficiency of memorizing the unit circle. Instead, it focuses on understanding two special triangles: the 45-45-90 and 30-60-90 triangles. The tutorial explains how to use these triangles to solve trigonometric problems without memorizing the unit circle. It provides techniques to simplify memorization by associating angles with their corresponding sides. The video concludes with tips for better understanding and invites viewers to ask questions for further clarification.

What is the main reason the video suggests not memorizing the unit circle?

• It is a waste of time compared to using special triangles.

• It is too complex to understand.

• It is not used in advanced mathematics.

• It is only applicable to certain problems.

What are the side lengths of a 45-45-90 triangle?

• 1, 1, 2

• 1, 1, square root of 2

• 1, 2, square root of 3

• 2, 2, square root of 3

Which triangle is used to find the cosine of 150 degrees?

• Equilateral triangle

• 30-60-90 triangle

• Isosceles triangle

• 45-45-90 triangle

How do you determine the reference angle for 150 degrees?

• Subtract 30 degrees from 180 degrees

• Add 30 degrees to 120 degrees

• Add 60 degrees to 90 degrees

• Subtract 60 degrees from 180 degrees

What is the tangent of negative 135 degrees?

• -1

• 1

• 0

• Undefined

Which triangle is used to find the tangent of negative 135 degrees?

• Equilateral triangle

• Scalene triangle

• 45-45-90 triangle

• 30-60-90 triangle

What is the relationship between angles and sides in a triangle?

• A small angle opens to a small side

• A large angle opens to a small side

• Angles and sides are unrelated

• A small angle opens to a large side

How can you determine the side lengths of a 30-60-90 triangle without memorization?

• By using the Pythagorean theorem

• By using trigonometric identities

• By matching the smallest angle to the smallest side

• By measuring with a ruler

What is the benefit of using special triangles over memorizing the unit circle?

• It requires less memorization and enhances understanding.

• It is faster to calculate.

• It is more accurate.

• It is applicable to all types of triangles.

Which side length corresponds to the largest angle in a 30-60-90 triangle?

• 2

• 1

• None of the above

• Square root of 3