Domain: describes all the values of that ‘x’ is able to take. Range: describes all the values that ‘y’ is able to take. Period: of a graph describes the part of a graph, which is periodically repeated. It uses the horizontal scale. Amplitude: of a ‘wave’ graph is the height of the wave fro the horizontal.

Relations Between the Trig Ratios sin θ = y tan θ = y/x Pythagorean Identities 1. tan θ = sin θ /cos θ 2. cot θ = cos θ /sin θ 3. cos² θ + sin² θ = 1 4. 1 + tan² θ = sec² θ 5. cot² θ + 1 = cosec² θ cos θ = x cot θ = x/y

Mathematics Summary Sheets – Trigonometry

2

Trig Equations We need: • • Domain: sinx cosx all real x all real x

Range: –1 ≤ sinx ≤ 1 -1 ≤ cosx ≤ 1 ∞ < tanx < ∞

• • • •

tanθ exists except for θ = ± 90°, ± 270°, ± 450° … ASTC results Special triangles (exact ratios) Results for 0°, 90°, 180°, 270°, 360°. B c A a C

Area of a triangle

A= ½absinC

Sine Rule a b c ______ = ______ = ______ sinA sinB sinC

...Teaching trigonometry using Empirical Modelling
0303417
Abstract
The trigonometric functions sin(x), cos(x) and tan(x) are relationships that exist between the angles
and length of sides in a right-angled triangle. In Empirical Modelling terms, the angles in a triangle
and the length of the sides are observables, and the functions that connect them are the definitions.
These well-defined geometric relationships can be useful when teaching GCSE-level students about
the...

...Right Triangle TrigonometryTrigonometry is a branch of mathematics involving the study of triangles, and has applications in fields such as engineering, surveying, navigation, optics, and electronics. Also the ability to use and manipulate trigonometric functions is necessary in other branches of mathematics, including calculus, vectors and complex numbers. Right-angled Triangles In a right-angled triangle the three sides are given special names. The side...

...Physics
Glossary
Electric circuit - one simple, complete conducting circuit pathway
Electronic gadget - a machine that consists of multiple circuits and transducers
Transducer – device that converts energy from one form to another
Input transducer – converts other forms of energy (sound, light, heat) into electrical energy, e.g. microphone
Output transducer – converts electrical energy into other forms of energy, e.g. speakers
Processor Component – found in electronic gadgets, receives...

...A Complicated Kindness SummarySheet
Core Mennonite Beliefs
* First and foremost: Christians
* Specific Mennonite philosophies
* Non violence
* No circumstances
* Mennonites are exempt from going to war
* Rejection of the world
* Should focus on heaven
* Things in real life are distractions
* Community
* Strong emphasis on doing charity and helping each other
* Putting faith...

...SPHERICAL TRIGONOMETRY
DEFINITION OF TERMS
The sphere is the set of all points in a three-dimensional space such that the distance of each from a fixed point is constant. The fixed point and the given distance are called the center and the radius of the sphere respectively.
The intersection of a plane with a sphere is a circle. If the plane passes through the center of the sphere, the intersection is a great circle; otherwise, the intersection is a small circle.
A...

...Early trigonometry
The ancient Egyptians and Babylonians had known of theorems on the ratios of the sides of similar triangles for many centuries. But pre-Hellenic societies lacked the concept of an angle measure and consequently, the sides of triangles were studied instead, a field that would be better called "trilaterometry".[6]The Babylonian astronomers kept detailed records on the rising and setting of stars, the motion of the planets, and the solar and lunar eclipses, all...

...ENGTRIG: LECTURE # 4.2 Spherical Trigonometry
Spherical Trigonometry
Engr. Christian Pangilinan
Areas of a Spherical Triangle
A=
π R2 E
180o E R
E = A + B + C − 180o
Where:
spherical excess radius of the sphere
Spherical Triangles Part of the surface of the sphere bounded by three arcs of three great circles Right Spherical Triangle – a spherical triangle containing at least one right angle
If the sides are known instead of the angles,...

...The Way Trigonometry is used in Astronomy
By: Joanna Matthews
Practical Applications of Advanced Mathematics
Mrs. Amy Goodrum
July 15, 2003
Abstract
This report is about how trigonometry is used in Astronomy. Even though trigonometry is applied in many areas, such as engineering, chemistry, surveying, and physics, it is mainly used in astronomy Trigonometry is used to find the distance of stars, the distance from one planet to...

1249 Words |
4 Pages

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