Unit 4 – Trigonomitry Quiz
True or False Questions, circle your answer.
1. cos(α)=opposite/adjacent true false
2. sin(54)=3.4/2.7 truefalse
for:
3. sin(α)/a=sin(β)/b is the same as a/sin(β)=b/sin(α)
true false
4. SohCahToa is not the same as primary trigonomic ratios
true false
5. The cosine law is: cos(γ)=(a²+b²c²)/(2ab)
true false
Multiple Choice, mark your answer(s).
1. sin(20°)=45.9/c
a.) c=88.79
b.) c=134.21
c.) c=50.28
d.) c=45.9/sin(20°)
2. How do you calculate the perimiter of a triangle?
a.) P=a²+b²c²
b.) A=bh/2
c.) P=a+b+c
c.) A=l*w
3. What would you use to find out x?
a.) the sine law
b.) sine the trigonomic ratio
c.) first the cosine law then the sine law
d.) first the sine law then tangent the trigonomic ratio 4. What is x from the triangle above?
a.) x=34.77°
b.) x= 97.5°
c.) x= 120.99°
d.) x=59.123°
5. You can definitely use SohCahToa if:
a.) you have 2 angles and an opposite angle
b.) you have 3 sides
c.) you have 2 angles and one side
d.) you have a right angled triangle
6.) sin(α)/a=sin(β)/b is:
a.) cosine law
b.) SohCahToa
c.) sine law
d.) tangent law
Give a short answer:
1. If you want to use the sine law to solve x, which sides and/or angles would you need? Explain.
I would need side c plus another one with the corresponding angle because for the sine law I need the side that corresponds to the wanted angle and another angle and side set. Here I could do: sin(x)/c=sin(α)/a or sin(x)/c=sin(β)/b. Another possibility is to have a, angle a and b, then I could find out angle b and subtract both known angles from 180°.
2. Explain how you would solve the triangle.
I would use the cosine law to find out c. Then I could use the sine law to find out either A or B. The left over angle I could find out by subtracting the ones I...
...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...
...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,...
...Maths Discussion
Our measures of the oval have given us a rough idea of what the perimeter and area is, however; it is not completely accurate. The reason for this is that we have figured out a very accurate perimeter for an irregular polygon inside the oval, but the perimeter of the oval will be greater than this because it is quite a lot larger (as we see in all the diagrams).
The task we had to carry out, however; for both the transverse, radial and hall diagram is very reasonably done because our measures for each angle and triangle add up to each other and the perimeter found from the radial and transverse survey are almost the same as each other. The transverse survey reveals the perimeter to be 316.19m and the radial survey suggests that the perimeter is 315.14m. Furthermore, to prove that the radial survey is accurate, all the 5 angles from around the oval add up to 360˚ which is essential to the results of the radial survey being accurate.
Our measurements for the height of the Minnamurra hall are accurate as well . This is because we used a trundle wheel to measure the distance of the line from the base of the wall to where we were measuring and we pointed the clinometer to the top of the hall and carefully checked the angle from the ground to the roof to find that it was 38˚. We drew this diagram up by using a simple rightangled triangle and labelling it’s base as being 13m and the small angle as being 38˚. We used ‘x’ to represent the...
...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...
...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...
...point, line, distance along a line, and distance around a circular arc.
4. Develop definitions of rotations, reflections, and translations in terms of angles, circles, perpendicular lines, parallel lines, and line segments.
5. Given a geometric figure and a rotation, reflection, or translation, draw the transformed figure using, e.g., graph paper, tracing paper, or geometry software. Specify a sequence of transformations that will carry a given figure onto another.
Similarity, Right Triangles, & Trigonometry GSRT
Define trigonometric ratios and solve problems involving right triangles
6. Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
7. Explain and use the relationship between the sine and cosine of complementary angles.
8. Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems.★
Apply trigonometry to general triangles
9. (+) Derive the formula A = 1/2 ab sin(C) for the area of a triangle by drawing an auxiliary line from a vertex perpendicular to the opposite side.
10. (+) Prove the Laws of Sines and Cosines and use them to solve problems.
11. (+) Understand and apply the Law of Sines and the Law of Cosines to find unknown measurements in right and nonright triangles (e.g., surveying problems, resultant forces).
Circles GC
2. Identify and describe...
...90
Score:
9 of 10 points
Answer Key
Top of Form
Question 1 (Worth 1 points)
(03.02)
Use the graph below to fill in the blank with the correct number:
f(2) = _______
Answer blank 1:
Points earned on this question: 1
Question 2 (Worth 2 points)
(03.02)<object:standard:macc.912.fif.1.3
Find f(5) for this sequence:
f(1) = 2 and f(2) = 4, f(n) = f(1) + f(2) + f(n  1), for n > 2.
f(5) = ______</object:standard:macc.912.fif.1.3
Answer blank 1:
Points earned on this question: 2
Question 3 (Worth 2 points)
(03.02)<object:standard:macc.912.fif.1.2
Laura rents a movie for a flat fee of $2.00 plus an additional $0.50 for each night she keeps the movie. Choose the cost function that represents this scenario if x equals the number of nights Laura has the movie.</object:standard:macc.912.fif.1.2
c(x) = 2.00x + 0.50
c(x) = 2.00 + 0.50x
c(x) = 2.50x
c(x) = (2.00 + 0.50)x
Points earned on this question: 2
Question 4 (Worth 1 points)
(03.02)<object:standard:macc.912.fif.1.2
If g(x) = x2 + 2, find g(3).</object:standard:macc.912.fif.1.2
9
8
11
6
Points earned on this question: 1
Question 5 (Worth 1 points)
(03.02)<object:standard:macc.912.fif.1.3
Generate the first 5 terms of this sequence:
f(1) = 0 and f(2) = 1, f(n) = f(n  1) + f(n  2), for n > 2.</object:standard:macc.912.fif.1.3
0, 1, 1, 0, 2
0, 1, 1, 2, 3
0, 1, 2, 2, 3
0, 1, 1, 2, 2
Points earned on this question: 1
Question 6 (Worth 1 points)
(03.02)<object:standard:macc.912.fif.1.2
Let...
...
ANALYSIS
Physics has a lot of topics to cover. In the previous experiments, we discussed Forces, Kinematics, and Motions. In this experiment, the focus is all about Friction. Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other. There are several types of friction like fluid friction which describes the friction between layers of a viscous fluid that are moving relative to each other; dry friction which resists relative lateral motion of two solid surfaces in contact and is subdivided into static friction between nonmoving surfaces, and kinetic friction between moving surfaces; lubricated friction which is a case of fluid friction where a fluid separates two solid surfaces; skin friction which is a component of drag, the force resisting the motion of a fluid across the surface of a body; internal friction is the force resisting motion between the elements making up a solid material while it undergoes deformation and sliding friction.
When surfaces in contact move relative to each other, the friction between the two surfaces converts kinetic energy into heat. This property can have dramatic consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Kinetic energy is converted to heat whenever motion with friction occurs, for example when a viscous fluid is stirred. Another important consequence of many types of friction can be wear,...