Unit Circle

Question 1

What is the unit circle?

Answer 1

A circle with a radius of 1.

Question 2

What is 90° in radian?

Answer 2

Question 3

How do you convert degrees to radian?

Answer 3

Question 4

How do you convert radian to degrees?

Answer 4

Question 5

What is 90° in radian?

Answer 5

Question 6

What is 30° in radian?

Answer 6

Question 7

What is 60° in radian?

Answer 7

Question 8

What is the Pythagorean Theorem?

Answer 8

Question 9

What is the formula for sin(θ) of a right triangle?

Answer 9

Question 10

What is the formula for tan(θ) of a right triangle?

Answer 10

Question 11

What is the formula for cos(θ) of a right triangle?

Answer 11

Question 12

How do you find the x-coordinate of a point on the unit circle?

Answer 12

cos(θ)

Question 13

How do you find the y-coordinate of a point on the unit circle?

Answer 13

sin(θ)

Question 14

How do we find the coordinates of points along the circumference of the unit circle?

Answer 14

Find the angle between the point and the x-axis through the origin, θ. Then the point is (cosθ, sinθ).

Question 15

Answer 15

Question 16

Answer 16

Question 17

Answer 17

Question 18

Answer 18

Question 19

In which quadrants do two different angles have the same sine?

Answer 19

Two angles have the same sine when they have the same y-coordinate. So, this is the same for quadrants 1 & 2 or for quadrants 3 & 4.

Question 20

In which quadrants do two different angles have the same cosine?

Answer 20

Two angles have the same cosine when they have the same x-coordinate. So, this is the same for quadrants 1 & 4 or for quadrants 2 & 3.

Question 21

When do two different angles have the same tangent?

Answer 21

When they are located 180° (or π) apart.

Question 22

How do you find the tangent of an angle that is *not* part of a right triangle?

Answer 22

Question 23

For what type of triangles can you use the Pythagorean Theorem?

Answer 23

Right triangles.

Question 24

What is a true bearing?

Answer 24

The true bearing of B from A is the clockwise measure of the angle between [AB] and the ‘north’ line through A.

For example:

Question 25

How can you use sine, cosine, or tangent to find an angle inside of a right triangle?

Answer 25

Question 26

What are the side lengths of a 45-45-90 triangle with hypotenuse length 1?

Answer 26

Question 27

What are the side lengths of a 30-60-90 triangle with hypotenuse length 1?

Answer 27