Enhance Your Learning with Trigonometric Ratios and Solving Triangles Flash Cards for quick learning
A branch of mathematics that deals with the relationships between the angles and sides of triangles.
The ratios of the lengths of the sides of a right triangle, which are used to solve various trigonometric problems.
In a right triangle, the ratio of the length of the side opposite the angle to the length of the hypotenuse.
In a right triangle, the ratio of the length of the side adjacent to the angle to the length of the hypotenuse.
In a right triangle, the ratio of the length of the side opposite the angle to the length of the side adjacent to the angle.
The reciprocal of the sine function: csc(theta) = 1/sin(theta).
The reciprocal of the cosine function: sec(theta) = 1/cos(theta).
The reciprocal of the tangent function: cot(theta) = 1/tan(theta).
An identity in trigonometry that relates the three basic trigonometric functions: sin^2(theta) + cos^2(theta) = 1.
One of the four regions into which the coordinate plane is divided by the x-axis and y-axis.
A circle with a radius of 1 unit, used to define trigonometric functions for any angle.
The acute angle formed between the terminal side of an angle in standard position and the x-axis.
Functions that relate the angles of a triangle to the ratios of the lengths of its sides.
The angle between the horizontal line of sight and the line of sight to an object above the horizontal line.
The angle between the horizontal line of sight and the line of sight to an object below the horizontal line.
A trigonometric law that relates the ratios of the sides of a triangle to the sines of its angles: a/sin(A) = b/sin(B) = c/sin(C).
A trigonometric law that relates the lengths of the sides of a triangle to the cosine of one of its angles: c^2 = a^2 + b^2 - 2ab*cos(C).
Equations that involve trigonometric functions and are solved using trigonometric identities and properties.
Equations that are true for all values of the variables involved, used to simplify trigonometric expressions and solve trigonometric equations.
Functions that give the angle whose trigonometric ratio is a given value, used to solve trigonometric equations and find unknown angles.
Formulas that express trigonometric functions in terms of other trigonometric functions, used to simplify trigonometric expressions and solve trigonometric equations.
Graphs that represent the values of trigonometric functions for different angles, used to visualize and analyze trigonometric functions.
The exact values of trigonometric ratios for certain special angles, such as 0 degrees, 30 degrees, 45 degrees, 60 degrees, and 90 degrees.
The values of trigonometric functions for any angle, obtained by using the unit circle and reference angles.
The values of trigonometric ratios for angles in the Cartesian plane, obtained by using the coordinates of points on the unit circle.
The application of trigonometric ratios to solve real-life problems, such as finding the height of a building or the distance between two objects.
Trigonometric identities that express the sine, cosine, and tangent of the sum or difference of two angles in terms of the sine, cosine, and tangent of the individual angles.
Trigonometric identities that express the sine, cosine, and tangent of twice an angle in terms of the sine, cosine, and tangent of the angle.
Trigonometric identities that express the sine, cosine, and tangent of half an angle in terms of the sine, cosine, and tangent of the angle.
Trigonometric identities that express the product of two trigonometric functions as the sum or difference of two trigonometric functions.
Trigonometric identities that express the sum or difference of two trigonometric functions as the product of two trigonometric functions.
Functions that repeat their values in regular intervals, such as trigonometric functions with a period of 360 degrees or 2π radians.
The maximum value of a periodic function, measured from the midline to the peak or trough.
The horizontal displacement of a periodic function, measured in degrees or radians.
The vertical displacement of a periodic function, measured in units.
Trigonometric equations that involve multiple angles, such as sin(2x), cos(2x), and tan(2x), and are solved using trigonometric identities and properties.
Trigonometric equations that can be rewritten in quadratic form, such as sin^2(x) + cos^2(x) = 1, and are solved using factoring or the quadratic formula.
Trigonometric equations that can be rewritten in exponential form, such as e^(ix) = cos(x) + i*sin(x), and are solved using logarithms or complex numbers.
Trigonometric equations that involve inverse trigonometric functions, such as sin^(-1)(x), cos^(-1)(x), and tan^(-1)(x), and are solved using algebraic manipulation and trigonometric identities.
Trigonometric equations that can be expressed in parametric form, such as x = a*cos(t) and y = b*sin(t), and are solved by eliminating the parameter.
Trigonometric equations that involve complex numbers, such as cos(x) + i*sin(x) = e^(ix), and are solved using Euler's formula and complex number operations.
Trigonometric equations that can be simplified by substituting trigonometric functions, such as x = sin(t) or x = tan(t), and are solved using algebraic manipulation and trigonometric identities.
Trigonometric equations that cannot be solved algebraically and require numerical methods, such as iteration or approximation, to find the solutions.
The use of trigonometry in various engineering fields, such as civil engineering, mechanical engineering, and electrical engineering, to solve problems related to angles, distances, forces, and vibrations.
The use of trigonometry in physics to analyze and solve problems related to motion, waves, oscillations, and forces, using concepts such as displacement, velocity, acceleration, frequency, and amplitude.
The use of trigonometry in navigation to determine the position, direction, and distance of objects or locations on the Earth's surface, using concepts such as latitude, longitude, bearings, and triangulation.
The use of trigonometry in architecture to design and construct buildings, bridges, and other structures, using concepts such as angles of elevation, angles of depression, and trigonometric ratios.
The use of trigonometry in astronomy to study celestial objects and phenomena, such as the positions, distances, and motions of stars, planets, and galaxies, using concepts such as parallax, angular size, and apparent magnitude.
The use of trigonometry in computer graphics to create and manipulate images, animations, and 3D models, using concepts such as rotation, translation, scaling, and perspective projection.
The use of trigonometry in music to analyze and create sounds, harmonies, and rhythms, using concepts such as frequency, amplitude, phase, and waveforms.
The use of trigonometry in sports to analyze and improve athletic performance, such as calculating distances, angles, speeds, and trajectories in sports like golf, baseball, basketball, and soccer.
The use of trigonometry in medicine to analyze and diagnose medical conditions, such as measuring blood pressure, heart rate, and respiratory rate, using concepts such as pulse oximetry and electrocardiography.
The use of trigonometry in geography to study and map the Earth's surface, such as measuring heights, distances, and angles in topographic surveys and satellite imagery.
The use of trigonometry in surveying to measure and map land, buildings, and other features, such as determining distances, elevations, and angles in land surveys and construction projects.
The use of trigonometry in cartography to create and interpret maps, charts, and globes, such as representing the Earth's surface on a flat map using projections and coordinate systems.
The use of trigonometry in photography to calculate exposure settings, such as shutter speed, aperture, and ISO, and to analyze and correct lens distortions and perspective distortions.