Algebra II - Chapter 9 Vocabulary
area of a sector
A = ½r²θ, where r is the radius and θ is the central angle measured in radians
reference angle
the positive acute angle formed by the terminal side of angle and x-axis
initial side
the ray on the x-axis
hypotenuse
the side across from the right angle in a triangle
Pythagorean Theorem
used to find missing side lengths in right triangles a² + b² = c²
special right triangles
30-60-90 triangle 45-45-90 triangle
unit circle
a circle with a radius of 1; can be used to calculate trigonometric ratios
right triangle
a triangle with a right angle
radian
a unit of angle measure based on arc length
angles in a triangle
always add up to 180°
acute angle
an angle that measures less than 90°
quadrantal angles
angle in standard position whose terminal side lies on an axis
standard position
angle is in this when its vertex is at origin and one ray is the positive x-axis
coterminal angle
angles formed by different rotations that have the same initial and terminal sides; can be found by adding or subtracting multiples of 360°
cosine
cos θ; ratio of the length of the adjacent leg to hypotenuse; CAH
angle of rotation
formed by rotating the terminal side and keeping the initial side in place; counterclockwise is positive and clockwise is negative
terminal side
other ray of an angle
secant
reciprocal to cosine; ratio of the length of the hypotenuse to adjacent leg;
cosecant
reciprocal to sine; ratio of the length of the hypotenuse to opposite leg;
cotangent
reciprocal to tangent; ratio of the length of the adjacent leg to opposite leg;
sector
region of a circle bounded by 2 radii and an arc
45-45-90 triangle
right triangle with side lengths of 1, 1, √2
30-60-90 triangle
right triangle with side lengths of 1, 2, √3
arc length
s = rθ, where r is the radius and θ is the central angle measured in radians
sine
sin θ; ratio of the length of the opposite leg to hypotenuse; SOH
tangent
tan θ; ratio of the length of the opposite leg to adjacent leg; TOA