6. Calculate the total magnification of an object viewed under a) the low power objective and b) the high power objective?

Slides:



Advertisements
Similar presentations
Right Angled Triangles
Advertisements

Trigonometry.
Trigonometry Right Angled Triangle. Hypotenuse [H]
 ∆ABC has three angles… › ∡C is a right angle › ∡A and ∡B are acute angles  We can make ratios related to the acute angles in ∆ABC A CB
Trigonometry Review of Pythagorean Theorem Sine, Cosine, & Tangent Functions Laws of Cosines & Sines.
Right Triangle Trigonometry Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 The six trigonometric functions of a.
Trigonometry and Vectors 1.Trigonometry, triangle measure, from Greek. 2.Mathematics that deals with the sides and angles of triangles, and their relationships.
Trigonometric Ratios Consider the triangle given below. 1.The box in the bottom right corner tells us that this is a right triangle. 2.The acute angle.
Trigonometry Obj: I can to use trigonometry to find unknown sides and unknown angles in a triangle. Trigonometry is concerned with the connection between.
EXAMPLE 5 Find leg lengths using an angle of elevation SKATEBOARD RAMP You want to build a skateboard ramp with a length of 14 feet and an angle of elevation.
Six Example with choice
Right Angle Trigonometry These relationships can only be used with a 90 o angle. SOH CAH TOA can be used to help remember the ratios A Adjacent Opposite.
Naming sides of a Right Angled Triangle Intro How to Identify Hypotenuse Opposite Adjacent Identify Sides in Triangles.
Lesson 7-5 Right Triangle Trigonometry 1 Lesson 7-5 Right Triangle Trigonometry.
{ Law of Sines and Cosines Trigonometry applied to triangles without right angles. 1.
Right Angle Trigonometry. Labeling a Right Triangle  In trigonometry, we give each side a name according to its position in relation to any given angle.
Get a calculator!. Trigonometry Trigonometry is concerned with the connection between the sides and angles in any right angled triangle. Angle.
Right Triangle Trigonometry
Warm-Up 3/24-25 What are three basic trigonometric functions and the their ratios? Sine: sin  Cosine: cos  Tangent: tan 
1 Practice Problems 1.Write the following to 4 decimal places A)sin 34 o = _____ B) cos 34 o = _____ C)tan 4 o = _____ D) cos 84 o = _____ E)tan 30 o =
Trigonometry functions and Right Triangles First of all, think of a trigonometry function as you would any general function. That is, a value goes in and.
Right Triangle Trigonometry Obejctives: To be able to use right triangle trignometry.
LESSON 3 – Introducing….The CAST Rule!!!
Set calculators to Degree mode.
Review of Trig Ratios 1. Review Triangle Key Terms A right triangle is any triangle with a right angle The longest and diagonal side is the hypotenuse.
TRIGONOMETRY BASIC TRIANGLE STUDY: RATIOS: -SINE -COSINE -TANGENT -ANGLES / SIDES SINE LAW: AREA OF A TRIANGLE: - GENERAL -TRIGONOMETRY -HERO’S.
Trigonometric Ratios and Their Inverses
Lesson 13.4, For use with pages cos 45º ANSWER 1 2 Evaluate the expression. 2. sin 5π 6 3.tan(– 60º) ANSWER – 3 ANSWER 2 2.
Holt McDougal Algebra 2 Right-Angle Trigonometry Holt Algebra 2Holt McDougal Algebra 2 How do we understand and use trigonometric relationships of acute.
13.4 and 13.5 Basic Trig. Today we will… Find the sine, cosine, and tangent values for angles. We will also use the sine, cosine and tangent to find angles.
Right Triangle Trigonometry Trigonometry is based upon ratios of the sides of right triangles. The six trigonometric functions of a right triangle, with.
Trigonometrical Ratios The ratio (fraction expressed as a decimal) of the length of one side of a RIGHT ANGLED TRIANGLE to the length of another side.
Introduction to Trigonometry Part 1
Trigonometry: The study of triangles (sides and angles) physics surveying Trigonometry has been used for centuries in the study.
World 5-1 Trigonometric Ratios. Recall that in the past finding an unknown side of a right triangle required the use of Pythagoras theorem. By using trig.
Chapter : Trigonometry Lesson 3: Finding the Angles.
1.2 Vectors in Two Dimensions Defining Vector Components Any vector can be resolved into endless number of components vectors. p. 11 DRDR DRDR D1D1 D2D2.
Resolution and Composition of Vectors. Working with Vectors Mathematically Given a single vector, you may need to break it down into its x and y components.
Title: Trigonometric Functions LEQ: What are the trigonometric functions and how are they used to solve right triangles?
Lesson 46 Finding trigonometric functions and their reciprocals.
Lesson 43: Sine, Cosine, and Tangent, Inverse Functions.
Warm Up 18° 10 cm x 55 x 9cm Find the length of sides x and y y.
 The study of triangles  Relationship between sides and angles of a right triangle › What is a right triangle? A triangle with a 90 ⁰ angle 90°
Component Vectors Vectors have two parts (components) –X component – along the x axis –Y component – along the y axis.
Ratios for Right Angle Triangles.  Sine = opposite hypotenuse  Cosine = opposite hypotenuse  Tangent = opposite adjacent Sin = OCos = ATan = O H H.
Starter Questions Starter Questions xoxo The Three Ratios Cosine Sine Tangent Sine Tangent Cosine Sine opposite adjacent hypotenuse.
Date: Topic: Trigonometric Ratios (9.5). Sides and Angles x The hypotenuse is always the longest side of the right triangle and is across from the right.
13.1 Right Triangle Trigonometry ©2002 by R. Villar All Rights Reserved.
Trigonometry Lesley Soar Valley College Objective: To use trigonometric ratios to find sides and angles in right-angled triangles. The Trigonometric.
Solving Right Triangles using Trigonometry. Labeling a Right Triangle  In trigonometry, we give each side a name according to its position in relation.
13.1 Right Triangle Trigonometry. Definition  A right triangle with acute angle θ, has three sides referenced by angle θ. These sides are opposite θ,
TRIGONOMETRY.
Trigonometry Learning Objective:
Trigonometry Trigonometry is concerned with the connection between the sides and angles in any right angled triangle. Angle.
Use of Sine, Cosine and Tangent
…there are three trig ratios
Trigonometry Learning Objective:
Trigonometry Obj: I can to use trigonometry to find unknown sides and unknown angles in a triangle. Trigonometry is concerned with the connection between.
…there are three trig ratios
Right Triangle Trigonometry
Trigonometry To be able to find missing angles and sides in right angled triangles Starter - naming sides.
Section 5.5 – Right Triangle Trigonometry
RIGHT OPPOSITE HYPOTENUSE ADJACENT HYPOTENUSE OPPOSITE ADJACENT
Trigonometry - Sin, Cos or Tan...
Right Triangle Trigonometry
Trigonometry (Continued).
All about right triangles
…there are three trig ratios
Trigonometry Olivia Miller.
Presentation transcript:

6. Calculate the total magnification of an object viewed under a) the low power objective and b) the high power objective?

 Supply check  Attendance  Remember to sign up for UT Quest and submit your “Test Paper” to turnitin.com  DUE TOMORROW  THIS IS THE EASIEST 100 YOU WILL EVER GET!

August 26, 2010

 A free body diagram is the visual representation of force vectors W OE = — mg N OS = + mg F OA = maf OS = µN ∑ F y = mg - mg = 0 ∑ F x = ma - µN = ma net F net = ma net

 #1 & 2 together  10 minutes to complete  #3 & 6 Groups 1, 4, 7  #4 & 7 Groups 2, 5, 8  #5 & 8 Groups 3, 6, 9

W OE = — mg N OS = + mg ∑ F y = N OS - W OE = 0 ∑ F y = mg - mg = 0

W OE = — mg N OS ∑ F ynet = N OS - W OE = ma net

W OE = — mg N OS = + mg F OA = ma ∑ F y = N OS - W OE = 0 = mg - mg = 0 ∑ F x = ma net

W OE = — mg N OS = + mg F OA = maf OS = µN ∑ F y = mg - mg = 0 ∑ F x = ma - µN = ma net F net = ma net

W OE = — mg N OS = + mg F OA = maf OS = µN ∑ F y = mg - mg = 0 ∑ F x = ma - µN = — ma net F net = — ma net

T OR = + mg W OE = — mg

T OR = + mg W OE = — mg F OA = ma

T OR = + mg W OE = — mg Can we directly measure the Tension? Is it still equal to +mg? Why or why not? -x +y The x and y are just the components of the actual forces. This is why they’re drawn with dotted lines. You must ALWAYS draw components with dotted lines. F OA = ma

 Trigonometry: deals with angles and sides of triangles  Sine  (sin  )  Opposite over  Hypoteneuse  C osine  (cos  )  Adjacent over  Hypoteneuse  T angent  (tan  )  Opposite over  A djacent  Y = Opp. X =Adj. Hyp.

x adj y opp T S O HC A HT O A i p y o d y a p d n p p s j pn p j sin Ѳ = opp = y hyp T cos Ѳ = adj = x hyp T tan Ѳ = opp = y adj x Ѳ

X T cos Ѳ =x adj Y T sin Ѳ = y opp T S O HC A HT O A i p y o d y a p d n p p s j pn p j T sin Ѳ = y T cos Ѳ = x Ѳ

T OR = + mg W OE = — mg -x T cos Ѳ =x +y T sin Ѳ = +y ∑ F y = T sin Ѳ - mg = 0 ∑ F x = ma - T cos Ѳ = 0 F OA = ma

W OE = — mg Ѳ Ѳ T OR2 T OR1 In order for this box to just be hanging, what does the upward y component of the tension HAVE to be??