The Primary Trig Ratios – Practice with SOH CAH TOA
1. In each triangle, name the side:
2. Calculate the Sin A and Sin B in each triangle.
3. Calculate.
a. Sin 42b. Cos 68c. Tan 12
4. Calculate the value of x.
a. b.
5. Calculate.
a. Sin0.612b. Cos 0.825c. Cosd. Tan
6. Calculate E to the nearest degree.
a. Sin E = 0.387 b. Sin E = 0. 900 c. Cos E = d. Tan E =
7. Calculate E.
8. A guy wire is 13.5 m long. It supports a vertical power pole. The wire is fastened to the ground 9.5 m from the base of an 8.7 m tall pole. Calculate the measure of the guy wire and the ground.
9. A 5.0 m ladder is leaning 3.7 m up a wall. What is the angle the ladder makes with the ground?
10. A kite has a string 100 m long anchored to the ground. The string makes and angle with the ground of 68. What is the horizontal distance of the kite from the anchor?
11. A ladder is leaned 10 m up a wall with its base 6 m from the wall. What angle does the ladder make with the ground?
12.An archer shoots and gets a bullseye on the target. From the archer’s eye level the angle of depression to the bullseye is 5°. The arrow is in the target 50 cm below the archer’s eye level. Calculate the distance the arrow flew to hit the target (the dotted line). 5°
C
B
50 cm
A
5°
C
B
50 cm
A
13.Two islands A and B are 3 km apart. A third island C is located due south of A and due west of B. From island B the angle between islands A and C is 33°. Calculate how far island C is from island A and from island B.
14.The foot (bottom) of a ladder is placed 1.5 m from a wall. The ladder makes a 70° angle with the level...
...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 rightangled 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 welldefined geometric relationships can be useful when teaching GCSElevel students about
the functions, as they provide a way to visualise what can be thought of as fairly abstract functions.
This paper looks at how different learning styles apply to Empirical Modelling, and presents a practical example of their use in a model to teach trigonometry.
1 Introduction
The trigonometric functions sin(x), cos(x) and tan(x)
are relationships that exist between the angles and
length of sides in a rightangled 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 welldefined geometric relationships can be useful when
teaching GCSElevel students about the functions,
as they provide a way to visualise what can be
thought of as fairly abstract functions. Rather than
teaching students by showing them diagrams in an
instructive way (already a good way of doing it), a
constructive approach may allow students to gain a
better understanding...
...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. Rightangled Triangles In a rightangled triangle the three sides are given special names. The side opposite the right angle is called the hypotenuse (h) – this is always the longest side of the triangle. The other two sides are named in relation to another known angle (or an unknown angle under consideration).
If this angle is known or under consideration
h
θ
this side is called the opposite side because it is opposite the angle
This side is called the adjacent side because it is adjacent to or near the angle Trigonometric Ratios In a rightangled triangle the following ratios are defined sin θ = opposite side length o = hypotenuse length h cosineθ = adjacent side length a = hypotenuse length h
tangentθ =
opposite side length o = adjacent side length a
where θ is the angle as shown
These ratios are abbreviated to sinθ, cosθ, and tanθ respectively. A useful memory aid is Soh Cah Toa pronounced ‘socartowa’
Page 1 of 5
Unknown sides and angles in right angled triangles can be found using these ratios. Examples Find the value of the indicated unknown (side...
...Trigonometry (from Greek trigōnon "triangle" + metron "measure"[1]) is a branch of mathematics that studies triangles and the relationships between the lengths of their sides and the angles between those sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies.[2] It is also the foundation of the practical art of surveying.
Trigonometry basics are often taught in school either as a separate course or as part of a precalculus course. The trigonometric functions are pervasive in parts of pure mathematics and applied mathematics such as Fourier analysis and the wave equation, which are in turn essential to many branches of science and technology. Spherical trigonometry studies triangles on spheres, surfaces of constant positive curvature, in elliptic geometry. It is fundamental to astronomy and navigation. Trigonometry on surfaces of negative curvature is part of Hyperbolic geometry.
Contents
f one angle of a triangle is 90 degrees and one of the other angles is known, the third is thereby fixed, because the three angles of any triangle add up to 180 degrees. The two acute angles therefore add up to 90 degrees: they are complementary angles. The shape of a triangle is completely determined,...
...Trigonometry (from Greek trigōnon "triangle" + metron"measure"[1]) is a branch of mathematics that studies triangles and the relationships between their sides and the angles between these sides. Trigonometry defines the trigonometric functions, which describe those relationships and have applicability to cyclical phenomena, such as waves. The field evolved during the third century BC as a branch of geometry used extensively for astronomical studies.[2] It is also the foundation of the practical art of surveying.
Trigonometry basics are often taught in school either as a separate course or as part of a precalculus course. The trigonometric functions are pervasive in parts of pure mathematics and applied mathematics such as Fourier analysis and the wave equation, which are in turn essential to many branches of science and technology. Spherical trigonometry studies triangles on spheres, surfaces of constant positive curvature, in elliptic geometry. It is fundamental to astronomy and navigation. Trigonometry on surfaces of negative curvature is part of Hyperbolic geometry.


\History
Main article: History of trigonometry
The first trigonometric tablewas apparently compiled byHipparchus, who is now consequently known as "the father of trigonometry."[3]
Sumerian astronomers introduced angle measure, using a division of...
...Trigonometry
 Introduction to trigonometryAs you see, the word itself refers to three angles  a reference to triangles. Trigonometry is primarily a branch of mathematics that deals with triangles, mostly right triangles. In particular the ratios and relationships between the triangle's sides and angles. It has two main ways of being used: 1. In geometryIn its geometry application, it is mainly used to solve triangles, usually right triangles. That is, given some angles and side lengths, we can find some or all the others. For example, in the figure below, knowing the height of the tree and the angle made when we look up at its top, we can calculate how far away it is (CB). (Using our full toolbox, we can actually calculate all three sides and all three angles of the right triangle ABC). 2. AnalyticallyIn a more advanced use, the trigonometric ratios such as as Sine and Tangent, are used as functions in equations and are manipulated using algebra. In this way, it has many engineering applications such as electronic circuits and mechanical engineering. In this analytical application, it deals with angles drawn on a coordinate plane, and can be used to analyze things like motion and waves. Chapter1Angles in the Quadrants( Some basic Concepts)In trigonometry, an angle is drawn in what is called the "standard position". The vertex of the angle is on the origin, and one side of the angle is fixed and drawn along the positive...
...students may ask to ”Read and Report”.
5. Kiera held the baby lovingly in her arms.
6. I’m afraid this plant won’t grow well in sandy soil .
7. Democracy is based on the idea that all people are equal .
8. Helen works to the best of her khowledge .
9. The doctor was accused of unprofessional behaviour .
10. A woman giving birth is often helped by a midwife .
11. After much debate a decision was reached that satisfied both parties.
12. We were quite happy that more than 50 people were at the meeting.
13. Who found Eton College in 1440?
14. Have you anyone at all that you can fill in?
15. The court’s rule is final, so Priestly will spend ten years in prison.
16. The students all show great interest in their school.
17. The Minister of Defence provided a short statement denying all knowledge of the affair.
18. The First Amendment of the law guarantees freedom of speech.
19. Not until 1789 was a united national government formed in the USA.
20. A boy in my class always shy when our teacher speaks to him.
21. Lynne was told that to avoid pregnancy she must go on the Pill.
22. Miss Hendricks will leave for Canada tomorrow.
23. Would you go if you were asked?
24. Can you open the window please?
25. The midwife says that labour may last some time.
Points (25) Comments
B. Insert one word in each gap to complete...
...us and our behaviour. They ape us therefore, it is very
crucial to watch ourselves and our responsibility to reinforce positive
behaviour and boost their selfesteem (Whitehead & Ginsberg, 1999).
5
BEd132: Positive Child Guidance
20120883 Juhi Mehta
To summarize, the role of a teacher is to provide the children the
conditions to learn and progress. To recognize each child as a unique learner
requires conditions and guidance to develop into a confident individual (NZTC,
2012). A child is best served when the relationships between the teacher and
parents are reciprocal and supportive.
6
BEd132: Positive Child Guidance
20120883 Juhi Mehta
Reference list:
Greenman, J. (2005, May). Places for childhood in the 21st century: A
conceptual framework. Beyond the Journal. Young Children on the
Web. Retrieved 20 December, 2006, from
http://www.journal.naeyc.org/btj/200505/01Greenman.pdf
Kaiser, B., & Rasminsky, J.S. (2003). Challenging behavior in young children:
Understanding, preventing, and responding effectively. Boston, MA:
Pearson Education, Inc.
Miller, D. F. (2007). Positive child guidance (5th ed.). Clifton Park, NY: Thomas
Delmar Learning.
Miller, D. F. (2010). Positive child guidance (6th ed.). Clifton Park, NY: Thomas
Delmar Learning.
New Zealand Tertiary College. (2012). Bed132: Positive Child Guidance
Retrieved February 1, 2014, from
http://www.nztc.ecelearn.com/lms/classroom/ViewStudyGuide.aspx?...
...odyArtworks are a reflection of the culture in which they are made. Throughout history, artists have manifestly depicted the society that surrounds them and as time has progressed, artists have continually alluded to the values and restrictions that society has placed. Manet’s Olympia, Judy Chicago’s Dinner Party and Orlan’s Orlan Gives Birth to her Loved Self, all represent various ideas and interest through the development of a visual language. As society has evolved, the depiction of the human body has gradually moved from the modest and passive representation of the Renaissance to the grotesque and visceral portrayals of the post modern era.
The Renaissance was a period astoundingly creative and intellectual. It was in this era that the convention of the reclining nude was established as a subject. Titian provides a paradigm demonstrating the values and practises of artists from this period. One of his most acclaimed works Venus of Urbino was later appropriated by the modernist artist Manet: Manet depicted the notion of defying the expectations of society. His works breached the codes of morality and tradition and he astounded many by the realness in his subjects. Manet created a work he thought would grant him a place in the pantheon of great artists. However, instead of following the accepted practice in French art, which dictates that paintings of the figure are to be modelled on historical, mythical, or biblical themes, Many chose to paint a woman of his time –...
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