Explain what a radian measure represents using the Unit Circle as a reference. A radian measure represents the distance of a radius on the unit circle from the positive x-axis. Radians are mostly associated with pi. 2) How do special right triangles directly relate to the circle? There are two types of special right triangles: 45-45-90 and 30-60-90.
Find the perimeter and area of the shaded sections of these shapes. (i) [7] (ii) [7] Total 60 marks Geometry and trigonometry Solutions to Topic assessment 1. The curve is a circle, centre O and radius 2. [2] 2. Substituting [pic] into [pic] gives [pic] Since the equation has a repeated root, the line meets the circle just once, and so the line is a tangent to the circle.
Week 5 - Assignment Week Five Written Assignment Following completion of your readings, answer the following two questions from “Chapter 12 Supplement” of Mathematics in Our World. Select one even problem from exercises 1 through 10 on page 810. Select one even problem from exercises 11 through 22 on pages 811-812. As you answer the questions above, identify what types of misrepresentation or misuse have been demonstrated by referring to the bold blue headings in the “Chapter 12 Supplement” (e.g., Suspect Samples, Asking Biased Questions, Misleading Graphs, etc.). The assignment must include (a) all math work required to answer the problems as well as (b) introduction and conclusion paragraphs.
7.1-7.6 Study Packet Best things to study for this upcoming test: #1 Your 7.1-7.3 and Radicals Test #2 THIS Study Packet #3 Your Notes and Worksheets, specifically on topics where you struggle #4 Your textbook. Yes, you can do assignments just for practice where the answers are given in the back of the book. As always, I’m available for help! 7.1 Area of Triangles and Parallelograms ________ 1) ________ 2) ________ 3) Find the height of a triangle given that the base length is 5cm and the area is 60cm2. 7.4 Area of Trapezoids, Kites and Rhombi ________ 4) ________ 5) ________ 6)
Wow, I am glad we use the shorter version of π =3.14 to solve our math problems but what is π really used for in today’s world? The obvious answer is π is used in almost every branch of math. If you want to find the circumference of a circle, the surface area of a cylinder, the area of a sector of a circle, any measurement of a circle, cylinder, or sphere it involves π since π was used to make the circle. So with that in mind, I thought I had a good handle on where π is used in the real world today. It is used by architects, contractors, draftsmen, building and bridge designers, engineers, or just about any job that uses shapes.
AP Calculus BC Ms. Nookala Name____________ In the AP Calculus BC course students will learn the following important topics: limits, derivatives, indefinite integrals, definite integrals, series and parametric equations. Students will know how to approach the problems numerically, graphically, analytically and verbally. Course Text Book Larson, Hostetler, Edwards. Calculus of a single variable. The 8th edition.
1.explain what a radian measure represents using the unit circle as a reference. -A radian measure on a unit circle is the measure of the length of the arc at certain points on the unit circle. 2.how do special right triangles directly relate to a unit circle. -On the unit circle the radius of the circle is also the hypotenuse. therefore if you set the hypotenuse to be a value such as 1. the side (x,y) of the triangle will be the sine and cosine values on the unit circle.
Composition and Inverse Functions MAT 222: Intermediate Algebra Instructor October 12, 2014 Composition and Inverse Functions Functions are helpful in algebra to determine model dependencies among different variables. For example, some situations require many levels of dependencies and are useful to express the final variable in terms of the first variable. Function composition defines a variable in terms of another one while reducing the level of dependencies; and an inverse function comes into play when checking a correlation between dependent and independent variables. This paper will outline and solve a true composition and inverse function. The functions are: fx=2x+5 gx=x2-3 hx=7-x3
Muslim mathematicians also adopted Arabic numerals from the Indians and used them in place-value system. Student Analysis What is the impact of these mathematical advances on Western Civilization? Document 5 Source: Using scientific observation and their understanding of mathematics and optics, Muslim scholars made advancement in trigonometry and astronomy as well as mapmaking. They used astrolabe (figure A) and the armillary sphere (Figure B) to study the skies and make calculations for their calendars and maps. Student Analysis How did these instruments impact Muslim and Western civilization?
Brunelleschi and the Origin of Linear Perspective http://www.mcm.edu/academic/galileo/ars/arshtml/arch1.html 1. How did Brunelleschi determine how to create a rational system for depicting space? He used linear perspective which allowed him to be able to create a realistic illusion of the 3 dimensional spaces on a 2 dimensional surface. This made it possible, with the help from mathematics, to represent reality of the artist and the physical reality of nature. He was the first to test out a series of optical experiments that led to his discoveries and findings.