Sec 2.5
... Inverse Tangent Function This function is commonly denoted in one of two ways: tan-1x or arctan(x) The meaning of this function is as follows for any number x between -1 and 1: tan-1x = arctan(x) = The angle between -/2 and /2 whose tangent is x. Think of the “answer” to the inverse cosine functio ...
... Inverse Tangent Function This function is commonly denoted in one of two ways: tan-1x or arctan(x) The meaning of this function is as follows for any number x between -1 and 1: tan-1x = arctan(x) = The angle between -/2 and /2 whose tangent is x. Think of the “answer” to the inverse cosine functio ...
Week 10 Math Vocabulary
... x intercept – the point where a graph crosses the x axis 2. y intercept – the point where a graph crosses the y axis 3. odds – the ratio of the number of ways an event can occur to the number of ways the event can not occur 4. skew lines – two lines in different planes that do not intersect ...
... x intercept – the point where a graph crosses the x axis 2. y intercept – the point where a graph crosses the y axis 3. odds – the ratio of the number of ways an event can occur to the number of ways the event can not occur 4. skew lines – two lines in different planes that do not intersect ...
Transforming Mathematics with GSP
... One major limitation is that the angle can only vary between 0 and 90º (or zero and π/2 radians). The trigonometric functions are functions of the angle (given in radians) and have an unlimited domain for the values of . Angle rotation around a circle can provide this unlimited ...
... One major limitation is that the angle can only vary between 0 and 90º (or zero and π/2 radians). The trigonometric functions are functions of the angle (given in radians) and have an unlimited domain for the values of . Angle rotation around a circle can provide this unlimited ...
Angles, Degrees, and Special Triangles
... • Given an angle θ in standard position and a point (x, y) on the terminal side of θ, then the six trigonometric functions of ANY ANGLE θ are can be defined in terms of x, y, and the length of the line connecting the origin and (x, y) denoted as r ...
... • Given an angle θ in standard position and a point (x, y) on the terminal side of θ, then the six trigonometric functions of ANY ANGLE θ are can be defined in terms of x, y, and the length of the line connecting the origin and (x, y) denoted as r ...
Chapter Five
... If P ( x, y ) is a point on the terminal side of any angle in standard position and if r x 2 y 2 is the distance from the origin to point P, then the six trigonometric functions of are defined as follows: y r x cos r y tan , x 0 x ...
... If P ( x, y ) is a point on the terminal side of any angle in standard position and if r x 2 y 2 is the distance from the origin to point P, then the six trigonometric functions of are defined as follows: y r x cos r y tan , x 0 x ...
inverse function
... Solving Right Triangles Use trigonometric ratios to find angle measures in right triangles and to solve real-world problems. ...
... Solving Right Triangles Use trigonometric ratios to find angle measures in right triangles and to solve real-world problems. ...
Sec 6.5
... If P ( x, y ) is a point on the terminal side of any angle in standard position and if r x 2 y 2 is the distance from the origin to point P, then the six trigonometric functions of are defined as follows: y r x cos r y tan , x 0 x ...
... If P ( x, y ) is a point on the terminal side of any angle in standard position and if r x 2 y 2 is the distance from the origin to point P, then the six trigonometric functions of are defined as follows: y r x cos r y tan , x 0 x ...
Trigonometric functions
In mathematics, the trigonometric functions (also called the circular functions) are functions of an angle. They relate the angles of a triangle to the lengths of its sides. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.The most familiar trigonometric functions are the sine, cosine, and tangent. In the context of the standard unit circle (a circle with radius 1 unit), where a triangle is formed by a ray originating at the origin and making some angle with the x-axis, the sine of the angle gives the length of the y-component (the opposite to the angle or the rise) of the triangle, the cosine gives the length of the x-component (the adjacent of the angle or the run), and the tangent function gives the slope (y-component divided by the x-component). More precise definitions are detailed below. Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers.Trigonometric functions have a wide range of uses including computing unknown lengths and angles in triangles (often right triangles). In this use, trigonometric functions are used, for instance, in navigation, engineering, and physics. A common use in elementary physics is resolving a vector into Cartesian coordinates. The sine and cosine functions are also commonly used to model periodic function phenomena such as sound and light waves, the position and velocity of harmonic oscillators, sunlight intensity and day length, and average temperature variations through the year.In modern usage, there are six basic trigonometric functions, tabulated here with equations that relate them to one another. Especially with the last four, these relations are often taken as the definitions of those functions, but one can define them equally well geometrically, or by other means, and then derive these relations.