More Trigonometry!! Section 4-2 Review Angles Standard Position
More Trigonometry!! Section 4-2 Review Angles Standard Position Coterminal Angles Reference Angles Converting from Degrees degrees, minutes, seconds (DMS) Angle- formed by rotating a ray about its endpoint (vertex)
Terminal Side Ending position Initial Side Starting position Standard Position Initial side on positive x-axis and the vertex is on the origin An angle describes the amount and direction of rotation 120 210 Positive Angle- rotates counter-clockwise (CCW) Negative Angle- rotates clockwise (CW)
Coterminal Angles: Two angles with the same initial and terminal sides Find a positive coterminal angle to 20 20 360 380 Find a negative coterminal angle to 20 20 360 340 Types of questions you will be asked: Identify a) ALL angles coterminal with 45, then b) find one positive coterminal angle and one negative coterminal angle. a) 45 + 360k (where k is any given integer). b) Some possible answers are 405, 765, - 315, - 675 Decimal Degrees (DD)
Decimal degrees are similar to degrees/ minutes/seconds (DMS) except that minutes and seconds are expressed as decimal values. Decimal degrees make digital storage of coordinates easier and computations faster. 60.34444 instead of 6020'40" Converting from DMS to DD Express 365010as decimal degrees (DD) To complete the calculation, remember that 1 degree = 60 minutes 1 minute = 60 seconds
20 minutes.= 0.33333 (20/60) 40 seconds = 0.01111 (40/3600) Add up the degrees to get an answer: 60 + 0.33333 + 0.01111=60.34444 DD Converting from DD to DMS Express 50.525 in degrees, minutes, seconds To reverse the process, we multiply by 60 instead. 50 + .525(60) 50 + 31.5 50 + 31 + .5(60) 50 degrees, 31 minutes, 30 seconds
Homework Page 238 # 2 - 16 evens So, what exactly is a RADIAN? Many math problems are more easily handled when degrees are converted to RADIANS. 5 For a visual depiction of a radian, lets look at a circle. Definition: a radian is an arc length of
one radius So, how many radians are there in a given circle? Whats the connection between degrees and radians? 6 4 3 a little extra
r 2 1 radia n 360 2 r 360 180 r 57.3 2
180 or We can use the two ratios to convert between radians and 180 degrees. Example: Change 330 to radians: 330
11 180 6 In most cases, radians are left in terms of 2 radians to degree measure. 3 2 180 120 3
Example: Convert Two formulas to know: 1. Arc Length of a circle: S = r ( in radians) ( ( in radians) in radians)) Example: Given a central angle of 128 degrees, find the length of the intercepted arc in a circle of radius 5 centimeters. Round to nearest tenth. S = r ( in radians) 2.
5 128 11.2 cm 180 Area of a sector (slice of pie): A = r2 ( in radians) ( ( in radians) in radians)) Example: Find the area of a sector of the central angle measures the radius of the circle is 16 inches. Round to nearest tenth. A=r 2 1
5 2 16 335.1in 2 2 6 radians and Linear & Angular Velocity Things that turn have both a linear velocity and an angular velocity. Things that Turn - Examples tire on a car or bike buckets on a waterwheel
teeth on a gear can on a kitchen cabinet lazy susan propeller on an airplane horse on a Merry-Go-Round fins on a fan or a windmill earth on its axis Linear & Angular Velocity - Examples film on a projector or tape on a videotape turntable in a microwave oven blade on a lawnmower Earth around the sun seat on a Ferris wheel rope around a pulley a record on an old record player
drum/barrel in a clothes dryer Things that Turn - Examples lock on your locker hands on a clock roller brush on a vacuum cleaner tops & gyroscopes & dradle motor crankshaft blades in a blender roller skate wheels Carnival rides: tilt-a-whirl, scrambler, etc. weather vane washing machine agitator Angular Velocity Definition:
Angular Velocity ():): the speed at which an angle opens. Remember: is in radians. Ex. 6 rev/min, 360/day, 2 rad/hour t Angular Velocity Example: determine the angular velocity if 7.3 revolutions are completed in 9 seconds. Round to nearest tenth. 1 revolution is 2 radians so were talking about
7.3 2 14.6 radians Lets use the formula: t 14.6 9.2rad / sec 9sec Angular Velocity EXAMPLE 2: A carousel makes 2 5/8 rotations per minute. Determine the
angular velocity of a rider on the carousel in radians per second . 2 85 2.625revolutions 2.625revs 1min 2 radians radians 0.275 1min 60sec revolution sec Linear Velocity Definition:
Linear Velocity: the speed with which An object revolves a fixed distance from a central point. If you already know the angular velocity, then Ex. 55 mph, 6 ft/sec, 27 cm/min, 4.5 m/sec v r t r Linear Velocity
In the carousel scenario, one of the animals is 20 feet from the center. What is its linear velocity? Solution The cable moves at a fixed speed a linear velocity. r t .275radians 20 sec 5.5 ft/sec
Functions of Eggs . ... Eggs serve as an interfering agent when they inhibit the formation of ice crystals as in ice cream (helps keep it creamy) To Give Structure, Flavor and Color . Structure: Eggs add structure to baked...
About IMS Institute for HealthcareInformatics. UnbiasedInformation. AcademicResearch. Public PolicySupport. Provide policy setters and decision-makers in the global health sector with unique and transformational insights related to healthcare dynamics derived from granular analysis ofinformation
MUA+MTA. MX Server. MUA. Spambot. Victim. Spambot initiate SMTP connection with recipient mail server. Direct-To-MX. The last method is to directly deliver the spam message to it the recipient's MX server. In this case spambots work as a client and...
Analogy. Comparison of items to compare the known to the unknown. Compares two things, which are alike in several respects, for the purpose of explaining or clarifying some unfamiliar or difficult idea or object by showing how the idea or...
The average amount of OSAP debt was just over $23,000 ($20,000 in 2007). OSAP loans, at 33% (42% in 2007) of total reported debt, are tied with bank loans to represent the single largest share of debt among those students...
• Dr. Chris Gaston, Group Leader, Markets and Economics, Forintek Canada • Mr. Lars-Goran Olsson, Marketing Specialist, Swedish Wood Association UNECE TIMBER COMMITTEE Fifty-ninth session 2-5 October 2001
Download and install Quartus II package and University Program Installer (Use Download Instruction from website). Do not do this in lab, it takes a while. Refer to . Getting Started with DE-series Boards.pdf . in the . Additional Materials ....
Numerical Measures * * Coefficient of Variation Example: Height vs. Weight In a class of 30 students, the average height is 5'5'' with a standard deviation of 3'' and the average weight is 120 lbs with a standard deviation of...
Ready to download the document? Go ahead and hit continue!