Using a 45 45 90 triangle evaluate trig functions

The video tutorial covers the construction and significance of special triangles, such as 45-45-90 and 30-60-90 triangles, in geometry. It explains the use of the Pythagorean theorem to determine side lengths and explores the relationships between the unit circle and right triangles. The tutorial also delves into trigonometric functions, including cotangent, cosine, and cosecant, and their relationships. Finally, it guides viewers on constructing special triangles based on given angles, emphasizing the importance of understanding these geometric relationships.

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

• 1 unit

• sqrt(2) units

• sqrt(3) units

• 2 units

In the unit circle, what is the value of 'a' if a^2 + a^2 = 1?

• sqrt(3)/2

• sqrt(2)/2

• 1/2

• 1

What is the cotangent of a 45-degree angle?

• 1/2

• sqrt(2)

• 0

• 1

How do you find the cosecant of an angle?

• 1/sine

• 1/cosine

• 1/tangent

• 1/cotangent

What is the cosine of a 45-degree angle in a 45-45-90 triangle?

• 1/2

• sqrt(2)/2

• 1

• sqrt(3)/2

When constructing a 30-60-90 triangle, what is the ratio of the sides opposite the 30, 60, and 90-degree angles?

• 1:sqrt(2):2

• 1:sqrt(3):2

• 1:1:sqrt(2)

• 1:2:sqrt(3)

Why is it important to construct special triangles accurately?

• To avoid using the Pythagorean theorem

• To simplify the unit circle

• To make the triangle look nice

• To ensure consistent trigonometric values