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Law of sines

In trigonometry, the law of sines (also known as the sine law, sine formula, or sine rule) is anequation relating the lengths of the sides of an arbitrary triangle to the sines of its angles. According to the law,

where a, b, and c are the lengths of the sides of a triangle, and A, B, and C are the opposite angles (see the figure to the right). Sometimes the law is stated using the reciprocal of this equation:

The law of sines can be used to compute the remaining sides of a triangle when two angles and a side are known—a technique known as triangulation. It can also be used when two sides and one of the non-enclosed angles are known. In some such cases, the formula gives two possible values for the enclosed angle, leading to an ambiguous case. The law of sines is one of two trigonometric equations commonly applied to find lengths and angles in a general triangle, the other being the law of cosines.

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Law of cosines

In trigonometry, the law of cosines (also known as the cosine formula or cosine rule) is a statement about a general triangle that relates the lengths of its sides to the cosine of one of itsangles. Using notation as in Fig. 1, the law of cosines states that

where γ denotes the angle contained between sides of lengths a and b and opposite the side of lengthc. The law of cosines generalizes the Pythagorean theorem, which holds only for right triangles: if the angle γ is a right angle (of measure 90° or π/2 radians), then cos(γ) = 0, and thus the law of cosines reduces to

The law of cosines is useful for computing the third side of a triangle when two sides and their enclosed angle are known, and in computing the angles of a triangle if all three sides are known. By changing which legs of the triangle play the roles of a, b, and c in the original formula, one discovers that the following two formulas also state the law of...

...APPLICATION OF SINELAW
The shorter diagonal of a parallelogram is 5.2 m. Find the perimeter of the parallelogram if the angles between the sides and the diagonal are 40o and 30o10’.
From the top of a 150 m lighthouse, the angles of depression of two boats on the shore are 20o and 50o, respectively. If they are due north of the observation point, find the distance between them.
SOLUTION
Solved for a
150/sin50 =...

...improve its throughput and power keeping the constraints in mind. This paper summarizes the CORDIC architectures, presents a simulation of basic CORDIC cell and Implements Unfolded CORDIC Architecture on Spartan XC3S50 FPGA family. Keywords— CORDIC, Sine, Cosine, FPGA, CORDIC throughput
III. In Section IV we discuss the implementation of CORDIC algorithm in an FPGA and the simulation of basic CORDIC cell using Xilinx tool and XC3S50 Spartan3 family of FPGA is...

...
PROPERTIES OF SINE AND COSINE FUNCTIONS:
1. The sine and cosine functions are both periodic with period 2π.
2. The sine function is odd function since it’s graph is symmetric with respect to the origin, while the cosine function is an even function since it’s graph is symmetric with respect to y axis.
3. The sine functions:
a. Increasing in the intervals[0, π/2]and [3π/2, 2π]; and
b....

...cos11π/12
cos(x/2) = ± √((1+cosx)/2) we use this Half-Angle Formula to evaluate it.
Since in this question, 11π/12 is in the Quadrant II, so cos(11π/12) should be negative.
cos11π/12 = – √((1+cos(11π/6))/2) = – √((1+(√3/2))/2)
to simplify it, both sides multiply by 2, – √(((1+(√3/2))(2))/((2)(2))) = – √((2+(√3))/4)
You should know what cos(11π/6) is, and you just plug in the number and you should get the answer.
(√3 – i)-10
We are using De Moivre’s Theorem to solve...

...Sine, Cosine, and Tangent Functions
Essential Questions: What is a function? How is the sine definition different from the sine function? Cosine? Tangent? From the graph of these functions, list some properties that describe them?
Rebecca Adcock, a former student of EMAT 6690 at The University of Georgia, and I agree that the concept of the Sine, Cosine Functions will occur at lesson 6 of a...

...TASK 1
Explain the reference to legal principle and relevant case law, the legal aspect of placing the ‘Klick’ clock in the shop window with a price tag attached.
Ann antiques has a rare ‘Klick’ clock on its shop with price tags of €1,000 attached. In spite of its wording the sign in the window does not constitute a legal offer, it is merely an invitation to treat. Invitation to treat is an indication that the person who invite is willing to enter into a negotiation but...

...
CENTRAL INSTITUTE OF TECHNOLOGY, KOKRAJHAR
(Centrally Funded Institute under MHRD, Govt. of India)
KOKRAJHAR::783370:: BODOLAND
Estd. :: 2006
A
Project Report
On
SINE AND COSINE FUNCTION GENERATOR
USING VHDL
Submitted by,
DHARMESWAR BORO
ROLL NO: Gau-c-10/L-322....

...This judgment is subject to final editorial corrections approved by the
court and/or redaction pursuant to the publisher’s duty in compliance
with the law, for publication in LawNet and/or the Singapore Law
Reports.
BNJ (suing by her lawful father and litigation
representative, B)
v
SMRT Trains Ltd and another
[2013] SGHC 286
High Court — Suit No 432 of 2011
Vinodh Coomaraswamy JC (as he then was)
29–31 October 2012; 1–2, 5–9, 19–20 November 2012; 11...

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