Trigonometry
... The flagpole, wire, and ground form a right triangle with the wire as the hypotenuse. Because you know an angle and the measures of its adjacent side and the hypotenuse, you can use the cosine ratio to find the height of the flagpole. height cos 35° = 20 ...
... The flagpole, wire, and ground form a right triangle with the wire as the hypotenuse. Because you know an angle and the measures of its adjacent side and the hypotenuse, you can use the cosine ratio to find the height of the flagpole. height cos 35° = 20 ...
Create your proportion!
... • Right Triangle – a triangle with one right angle and two acute angles. • Hypotenuse – the longest side in a right triangle. The hypotenuse is always across from the right angle. • Legs – the two other sides in a right triangle that form an “L” and create the right angle. • Opposite Side – The side ...
... • Right Triangle – a triangle with one right angle and two acute angles. • Hypotenuse – the longest side in a right triangle. The hypotenuse is always across from the right angle. • Legs – the two other sides in a right triangle that form an “L” and create the right angle. • Opposite Side – The side ...
PC6-2Notes.doc
... cot θ = 11/6 ; sec θ = 157 /11 ; csc θ = 157 /6 There are two basic right triangles whose ratios assist us in determining the values of trig functions. One of these is the 30-60-90 triangle. If you drew an equilateral triangle with side lengths 2 and bisect one of the angles so that this line is per ...
... cot θ = 11/6 ; sec θ = 157 /11 ; csc θ = 157 /6 There are two basic right triangles whose ratios assist us in determining the values of trig functions. One of these is the 30-60-90 triangle. If you drew an equilateral triangle with side lengths 2 and bisect one of the angles so that this line is per ...
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... ∗ hEuclideanGeometryOfPlanei created: h2013-03-21i by: hmattei version: h36962i Privacy setting: h1i hTopici h51-01i † This text is available under the Creative Commons Attribution/Share-Alike License 3.0. You can reuse this document or portions thereof only if you do so under terms that are compati ...
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.