Precalculus Vocab Chapter 4
Unit circle (p.247)
A circle of radius 1 centered at the origin of a coordinate system
Periodic functions (p.250)
A function with values that repeat at regular intervals. There exists a positive real number c such that f(t+c)=f(t) for all values of t in the domain of f
Oblique Triangles (p.291)
A triangle that is not a right triangle
Circular functions (p.248)
A trigonometric function defined as a function of the real number system using the unit circle
Radian (p.232)
A unit of angular measurement equal to 180°/π or about 57.296°
Quadrantal Angle (p.243)
An angle in standard position that has a terminal side that lies on one of the coordinate axes
Coterminal angles (p.234)
Angles in standard position that have the same initial and terminal side, but different measures.
Period (p.250)
For a function y=f(t), the smallest positive number c for which f(t+c) = f(t)
Ambiguous case (p.292)
Given the measures of two sides and a non-included angle, either no triangle exists, exactly one triangle exists, or two triangles exist
Law of sines (p.291)
If triangle ABC has side lengths a,b, and c representing the lengths of the sides opposite the angles with measures A,B, and C, respectively, then sinA/a = sinB/b = sinC/c
Law of cosines (p.295)
If triangle ABC has side lengths a,b, and c representing the lengths of the sides opposite the angles with measures A,B, and C, respectively, then the following are true. a^2 = b^2 + c^2 - 2bc cos(A) b^2 = a^2 + c^2 − 2ac cos(B) c^2 = a^2 + b^2 − 2ab cos(C)
Heron's formula (p.296)
If triangle ABC has side lengths a,b, and c, then the area of the triangle is sqrt(s(s-a)(s-b)(s-c)), where s=1/2(a+b+c).
Inverse cosine (p.223)
If θ is an acute angle and the cos θ = x, then the inverse cosine of x, or cos-1 x is the measure of angle θ.
Inverse sine (p.223)
If θ is an acute angle and the sin θ = x, then the inverse sine of x, or sin-1 x is the measure of angle θ.
Inverse tangent (p.223)
If θ is an acute angle and the tan θ = x, then the inverse tangent of x, or tan-1 x is the measure of angle θ.
Sector (p.237)
In a circle, the region bounded by a central angle and its intercepted arc
Secant (p.220)
In a right triangle with acute angle θ, the ratio comparing the length of the hypotenuse to the side adjacent to θ. It is the reciprocal of the cosine ratio, or sec θ = 1/cosθ
Cosecant (p.220)
In a right triangle with acute angle θ, the ratio comparing the length of the hypotenuse to the side opposite θ. It is the reciprocal of sine ratio, or csc θ = 1/sinθ
Cosine (p.220)
In a right triangle with acute angle θ, the ratio comparing the length of the side adjacent θ and the hypotenuse. If θ is an acute angle and the cosine of θ is x, then the cosine of x is the measure of angle θ
Sine (p.220)
In a right triangle with acute angle θ, the ratio comparing the length of the side opposite θ and the hypotenuse. If θ is an acute angle and the sine of θ is x, then the sine of x is the measure of angle θ.
Tangent (p.220)
In a right triangle with acute angle θ, the ratio comparing the length of the side opposite θ and the side adjacent to θ. Let θ be an acute angle in a right triangle and the abbreviations opp, adj, and hyp refer to the lengths of the side opposite θ, the side adjacent to θ, and the hypotenuse, respectively. Then tan (θ) = opp/adj
Cotangent (p.220)
In a right triangle with acute angle θ, the ratio comparing the side adjacent to θ and the side opposite θ. It is the reciprocal of the tangent ratio, or cot θ = 1/tanθ
Standard position (p.231)
In the coordinate plane, an angle positioned so that its vertex is at the origin and its initial side is along the positive x-axis
Trigonometric Functions (p.220)
Let θ be an acute angle in a right triangle and opp, adj, and hyp are the lengths of the side opposite θ, the side adjacent to θ, and the hypotenuse, respectively. Then the trigonometric functions of θ are defined below.
Trigonometric Ratios (p.220)
Ratios that are formed using the side measures of a right triangle and a reference angle θ.
Reference Angle (p.244)
The acute angel formed by the terminal side of an angle in standard position and the x-axis
Angle of Elevation (p.224)
The angle formed by a horizontal line and an observer's line of sight to an object above.
Angle of Depression (p.224)
The angle formed by a horizontal line and an observer's line of sight to an object below.
Vertex (p.231)
The common endpoint of two or more nonlinear rays
Terminal side (p.231)
The final position of a ray after rotation when forming an angle.
Inverse Trigonometric Functions (p.223)
The inverse sine of x or sin-1 x, the inverse cosine of x or cos-1 x, and the inverse tangent of x or tan-1 x.
Linear speed (p.236)
The rate at which an object moves along a circular path
Angular speed (p.236)
The rate at which the object rotates about a fixed point
Initial side (p.231)
The starting position of a ray when forming an angle.
Solve a right triangle (p.226)
To find the measures of all of the sides and angles of a right triangle.
Reciprocal Function (p.220)
Trigonometric functions that are reciprocals of each other.