Radians, Special Angles, and Unit Circles
What are the coordinates for a 180 degree angle?
(-1, 0)
What are the coordinates for 270 degree angle?
(0, -1)
What are the coordinates for a 90 degree angle?
(0, 1)
What are the coordinates for a 0 or 360 degree angle?
(1,0)
What does 1 radian equal?
180 / π = 57. 3 degrees
π / 1 =
180 degrees
π radians is how many degrees?
180 degrees = half of a circle
cos^(-1)
1st quad, 2nd quad
sin ^(-1)
1st quad, 4th quad
tan^(-1)
1st quad, 4th quad
π / 6 =
30 degrees
A full circle is how many degrees? How many radians?
360 degrees 2π radians
π / 4 =
45 degrees
π / 3 =
60 degrees
π / 2 =
90 degrees
What is a radian?
An angle drawn between 1 radius drawn on the outside of the circle; it's an ANGLE MEASURE
The Law of Cosines
In any triangle, c² = a² + b² - 2ab(cos C)
The Law of Sines
In any triangle, sin A/a = sin B/b = sin C/c
What is a reference angle?
an acute, positive angle formed by the x axis and terminal side of the given angle
unit circle
circle with radius = 1, center at origin
What are the angles 0, 90, 180, and 360 called?
quadrant angles
sine, cosine, and tangent of 0
sin = 0 cos = 1 tan = 0
sine, cosine, and tangent of 90
sin = 1 cos = 0 tan = undefined
sine, cosine, and tangent of 30
sin = 1/2 cos = √3/2 tan = √3/3
sine, cosine, and tangent of 45
sin = √2/2 cos = √2/2 tan = 1
sine, cosine, and tangent of 60
sin = √3/2 cos = 1/2 tan = √3
Reference angle and original angle will have the same ... and ... measures but ... might be different
sine and cosine measures (absolute value), signs
In a unit circle, cosine A =
x = run
In a unit circle, sine A =
y = rise
In a unit circle, tangent A =
y/x = slope