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