Unit Circle Flashcards
What is the unit circle?
A circle with a radius of 1.
What is 90° in radian?
How do you convert degrees to radian?
How do you convert radian to degrees?
What is 90° in radian?
What is 30° in radian?
What is 60° in radian?
What is the Pythagorean Theorem?
What is the formula for sin(θ) of a right triangle?
What is the formula for tan(θ) of a right triangle?
What is the formula for cos(θ) of a right triangle?
How do you find the x-coordinate of a point on the unit circle?
cos(θ)
How do you find the y-coordinate of a point on the unit circle?
sin(θ)
How do we find the coordinates of points along the circumference of the unit circle?
Find the angle between the point and the x-axis through the origin, θ. Then the point is (cosθ, sinθ).
In which quadrants do two different angles have the same sine?
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.
In which quadrants do two different angles have the same cosine?
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.
When do two different angles have the same tangent?
When they are located 180° (or π) apart.
How do you find the tangent of an angle that is *not* part of a right triangle?
For what type of triangles can you use the Pythagorean Theorem?
Right triangles.
What is a true bearing?
The true bearing of B from A is the clockwise measure of the angle between [AB] and the ‘north’ line through A.
For example:
How can you use sine, cosine, or tangent to find an angle inside of a right triangle?
What are the side lengths of a 45-45-90 triangle with hypotenuse length 1?
What are the side lengths of a 30-60-90 triangle with hypotenuse length 1?
