Algebra II - Chapter 9 Vocabulary

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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


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