LSU Placement Exam Overview Study Guide - Plane Trigonometry | MATH 1022, Study notes of Trigonometry

Download LSU Placement Exam Overview Study Guide - Plane Trigonometry | MATH 1022 and more Study notes Trigonometry in PDF only on Docsity! LSU Trigonometry Placement Exam Crash Course Overview Created by Professor Jaron Burden This overview is broken into three (3) main topics of study for the exam. Each bolded and underlined topic is a hyper link to the corresponding page. Purplemath is a great resource for additional understanding of a topic. Google is also a great resource. Now the goal here is a speed lesson in trigonometry but ASK QUESTIONS IF YOU HAVE THEM! As a professor, it is my job to benefit my students in the most efficient way. Trigonometric Functions 1) Conversion between degrees and radians 2) Arc length 3) Finding the values of trigonometric functions of acute angles 4) Applications 5) Computing the values of trigonometric functions of given angles 6) Trigonometric functions of general angles 7) The unit circle 8) Graphs of trigonometric functions Analytic Trigonometry 9) Inverse trigonometric functions 10) Trigonometric identities 11) Sum and difference formulas 12) Double-angle and half-angle formulas 13) Trigonometric equations Applications of Trigonometric Functions 14) The Law of Sines 15) The Law of Cosines 16) Area of a triangle 1) 1.1Converting between degrees and radians So, you remember that unit circle, the one I put a picture of over there? Well that will help you understand this easy topic. Once around the unit circle is 360° but we could also say 2π. That, however, can be simplified to 180° = π. Real complex math, I know. Note, most times you see π, it’s referring to radians. Since we have that little fact up there, we can now convert between degrees and radians. Example J) A girl is riding her futuristic bike. When she makes a turn, it gives her the angle of her turn in radians. After making a sharp v-turn, the bike reads π 4 radians. She comes up to you and asks you to tell her the degrees because you look smart. Well are you? Convert the angle to degrees. Stumped? Well I’m nice so, I’ll help you out. So we know that she turned at π 4 radians. To change to degrees, we have to get rid of that blasted π. Well knowing that π = 180° we can use that ratio to get rid of π, by multiplying it (since its 1 to 1). π 4 ∗180 ° π = 180° 4 , which can be simplified down to 45°. Why she cares about that information, I don’t know. Now time to convert degrees to radians. Example A) You’re riding your futuristic bike blah blah blah it tells you 245°. Convert the degree measurement to radians. In this problem, we want the π, but not the degree. Using that same conversion factor, we’ll flip it then multiply. Pull to Reveal! Pull to Reveal! No, it’s not drawn exact. Think of this clock as a unit circle. A full rotation is 60 minutes, but we’re only moving 45 minutes creating an angle. Simple math shows that the ratio of 45 to 60 is the same as 3 to 4 or ¾. Now that we have that, we can find the radians of ϴ. (Btw, a shortcut to doing this is remembering the unit circle. ¾ of the unit circle is 3 π 2 ) Because some old guy said it, 2π rad is equal to 1 full revolution. Using that, we’ll multiply 2π rad by ¾ to get the radians of only the distance the minute hand will travel (45 minutes or ¾ the full revolution). ϴ = 45 60 * 2π rad = 45 π 30 rad = 3 π 2 rad Ready to finish this problem? I definitely am. S = rϴ = (5in)( 3 π 2 rad) = 15 π 2 in (the radian is kind of a unit place holder) Take a break, you probably need one. Ready? I hope so, because to pass that exam you’ll need a more difficult problem. Example N) Ah, the mighty pendulum. Kids these days probably don’t know what they are. Anyway, a pendulum swings through an angle of 30° every second. If the pendulum is 24 inches long, how far does its tip move each second? Pull t Reveal! 45 minutes 5 inches Did you draw a picture? That might help you take a swing at this problem (pendulum pun!). This problem actually isn’t that difficult. Let’s use our standard equation S = rϴ, and identify our variables. The length of the pendulum is our radius. Notice that wherever the tip goes, it is always equidistant (the same distance) from the center of what appears to be a board. r = 24 in, and the angle we are given is 30° so that will be our ϴ. From here it is a matter of preference to finish the problem with a degree measurement or a radian. Might as well do radian. ϴ = 30° * π 180° (we didn’t use 2π rad because the pendulum doesn’t attempt to make a full revolution) ϴ = π 6 Now let’s finish this. S = rϴ = (24 in)( π 6 ) = 4π in ≈ 12.56 in Almost done with this section, I promise. Now it is time for Area of a Sector of a Circle. Pull to Reveal! 30° 24 inches