Exploring 45-45-90 Triangles and Trigonometric Functions

The video tutorial explains the properties of the 45-45-90 triangle, a special isosceles right triangle. It covers the side ratios of 1, 1, and the square root of 2, which are crucial for calculating trigonometric functions like sine, cosine, and tangent for 45 degrees. The tutorial demonstrates how to rationalize these values and discusses the relationships between tangent, cosecant, secant, and cotangent for 45 degrees, emphasizing their equivalence and congruence.

What type of triangle is a 45-45-90 triangle?

• Acute

• Scalene

• Isosceles right

• Equilateral

What is the length of the hypotenuse in a 45-45-90 triangle if the legs are each 1 unit?

• 1.5

• 2

• 1

• Square root of 2

Which of the following is not a property of a 45-45-90 triangle?

• All sides are of equal length

• It has one angle of 90 degrees

• It is an isosceles triangle

• All angles are 45 degrees

How is the sine of 45 degrees calculated using the 45-45-90 triangle?

• Hypotenuse divided by leg

• Opposite side divided by adjacent side

• Leg divided by hypotenuse

• Adjacent side divided by opposite side

What is the value of cosine 45 degrees after rationalization?

• 1/2

• Square root of 2 over 2

• Square root of 2

• 1

What is the value of tangent 45 degrees?

• 2

• 1

• 0

• Square root of 2

What is the cosecant of 45 degrees?

• 1

• 2

• Square root of 2

• 1/2

Which of the following is true for the secant of 45 degrees?

• 1/2

• 1

• 2

• Square root of 2

What is the relationship between tangent and cotangent at 45 degrees?

• They are unrelated

• They are reciprocals

• They are equal

• Cotangent is double the tangent

What is the value of cotangent 45 degrees?

• 2

• Square root of 2

• 1

• 0