10/24/22 - Special Triangles, Sine and Cosine of Angles

Question 1

What are the lengths of the legs of a 45-45-90 right triangle with hypotenuse 1?

Answer 1

√2/2

Question 2

What are the lengths of the legs of a 30-60-90 right triangle with hypotenuse 1?

Answer 2

1/2 and √3/2

Question 3

What is a reference triangle?

Answer 3

Corresponding to angle θ on the unit circle, a reference triangle has vertices at (0, 0); (cos θ, 0); and (cos θ, sin θ)

Question 4

What is a reference angle?

Answer 4

An interior angle at the origin of a reference triangle.

Question 5

What are the coordinates of points on the unit circle at 0, 90, 180, and 270 degrees?

Answer 5

0 deg: (1, 0)
90 deg: (0, 1)
180 deg: (1, 0)
270 deg: (0, -1)

Question 6

What are the coordinates of points on the unit circle at 45, 135, 225, and 315 degrees?

Answer 6

45 deg: (√2/2, √2/2)
135 deg: (-√2/2, √2/2)
225 deg: (-√2/2, -√2/2)
315 deg: (√2/2, -√2/2)

Question 7

What are the coordinates of points on the unit circle at 30, 150, 210, and 330 degrees?

Answer 7

30 deg: (√3/2, 1/2)
150 deg: (-√3/2, 1/2)
210 deg: (-√3/2, -√3/2)
330 deg: (√3/2, -√3/2)

Question 8

What are the coordinates of points on the unit circle at 60, 120, 240, and 300 degrees?

Answer 8

60 deg: (1/2, √3/2)
120 deg: (-1/2, √3/2)
240 deg: (-1/2, -√3/2)
300 deg: (1/2, √3/2)