# Grade 10 IB - Math - Trig

Flashcards by Lauren Jatana, updated more than 1 year ago
 Created by Lauren Jatana over 5 years ago
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### Description

Flashcards on Grade 10 IB - Math - Trig, created by Lauren Jatana on 10/29/2015.

## Resource summary

 Question Answer What is the main concept of trigonometry to relate angles with sides of a triangle? No matter the size of the triangle, if the RATIO of the sides are the same, the angle will be the. E.g. 1/2 of left and bottom is the same angle as 2/4 or 4/8! So if 1:2 (left to bottom) triangle has the same angle as a 4:8 triangle (left to bottom), - then what might we say trig is all about? 1:2 means ratio of left to bottom length. And the ratio can also be represented 3 ways - like a fraction 1/2. That means, trig is ALL about RATIOS =) What are the main 3 trig "ratios" called? (*looks at calculator*) And how do you pronounce them? Sin(x) = "Sine OF x" (Don't for get the OF) Cos(x) = "Cos OF x" Tan(x) = "Tan OF x" There are 3 more trig ratios that you will need to know in the future... can you remember what their names are, and how to 'make them'? 1/sin(x) = cosecant(x) "co-secant OF x" 1/cos(x) = secant(x) 1/tan = cotangent So if trig is RATIOS OF SIDES of TRIANGLES, then what are - cos, sin and tan doing in the mix? Duh, they must be ratios then too! different kinds of ratios, each ratio of different PARTS of the triangle. What are cos, sin and tan ratios then? SOH CAH TOA S=O/H C=A/H T=O/A Ratios of different parts of the triangle. How do you know which part of the triangle is O, A or H ???? (What is O, A and H again?) O=opposite, A=Adjacent, H=Hypotenuse ***It all depends where you are "standing", which corner are you standing at is decided by whichever angle you are looking at. O= Opposite from where you're standing A=Adjacent (fancy for "beside") to you H=Hypotenuse, AKA Hippo!!! (Biggest side) PRACTICE TIME: 1. Label O, H and A 2. Which trig ratio is biggest in this triangle? Hint: you are standing at the bigger angle (not 90) 1. Where am I standing? Oh yeah, at the unlabelled angle - so left side = A, Right side is O, and bottom is the hippo, hypotenuse. 2. Cos = 3/5, Sin = 4/5 and Tan What is the requirement to use all SOH CAH TOA ratios? **What is the assumption you make when you use Sin, Cos, Tan? I assume that the triangle is a RIGHT triangle, any other triangle won't work!! Tan is just a poser. It doesn't have it's own personality. Why would I say that? Tan = Sin/Cos This means that you can always get TAN if you only know Sin and Cos!!! This is so helpful when you aren't given enough info. PRACTICE: What is the secret trick to this triangle? (Why can't we use normal SOH CAH TOA here?!) Imagine angle K is 20 degrees. What is the AREA of this triangle? Base is 10m long. 1. This is Isocolese! Yeah great job for noticing... so it means sides and angles are same. 2. Cant use SOH CAH TOA, because not RIGHT triangle 3. THE TRICK IN MATH: not a right triangle, so divide in half! 4. A(triangle) = (b*h)/2 So I have base, need h. 5. To get height, h, I will use trig ratios! I have Adjacent and need Opposite (Tan (20)= O/A, so Tan(20) = O/ 10 ... O=3.6m! (one equation, one unknown, good to go!) PRACTICE: Tricky! Sin(x) = 5/8 x=38 degrees! *did you remember the trick on the calculator? What is the 30 degrees, 60 degrees, 90 degrees triangle to memorize? 1, 2, /3 *Always check your memory with Pythagorus theorem What is the 45 degree triangle to memorize? 1, 1, /2 What should I remember when labelling an angle from a word problem? The wording e.g "32 degrees with the ground" or "ladder is leaned at 72 degrees with the wall" How do I know what is opposite and adjacent labels on the triangle? Depends on WHICH angle is of interest, and if an angle is even necessary.

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