Download presentation

Presentation is loading. Please wait.

Published byEan Coldwell Modified over 2 years ago

1
Slopes and Areas Frequently we will want to know the slope of a curve at some point. Or an area under a curve. We calculate area under a curve as the sum of areas of many rectangles under the curve. We calculate slope as the change in height of a curve during some small change in horizontal position: i.e. rise over run

2
Review: Axes When two things vary, it helps to draw a picture with two perpendicular axes to show what they do. Here are some examples: y x x t y varies with x x varies with t Here we say “ y is a function of x”. Here we say “x is a function of t”.

3
Positions We identify places with numbers on the axes The axes are number lines that are perpendicular to each other. Positive x to the right of the origin (x=0, y=0), positive y above the origin.

4
Straight Lines Sometimes we can write an equation for how one variable varies with the other. For example a straight line can be described as y = ax + b Here, y is a position on the line along the y-axis, x is a position on the line along the x- axis, a is the slope, and b is the place where the line hits the y-axis

5
Straight Line Slope y = ax + b The slope, a, is just the rise y divided by the run x. We can do this anywhere on the line. So the slope of the line here is y = -3 x 2 Remember: Rise over Run and up and right are positive Proceed in the positive x direction for some number of units, and count the number of units up or down the y changes

6
y- intercept y = ax + b is our equation for a line b is the place where the line hits the y-axis The intercept b is y = +3 when x = 0 for this line

7
We want an equation for this line y = ax + b is the general equation for a line So the equation of the line here is y = - 3 x + 3 2 Equation of our example line We plugged in the slope and y intercept

8
Intersecting Lines Intersecting lines make equal angles on opposite sides of the intersection If a line intersects two parallel lines, equal angles are formed at both intersections.

9
Intersecting Lines The sum of angles on one side of a line equals 180 o P1 If angle AOB is 50 o, what is angle COD? P2 If angle AOB is 50 o, what is angle COB?

10
Sum of angles in a Triangle The sum of angles in a triangle equals 180 o Notice this is a right triangle, because one of the angles (X0Y) is 90 o P3 if angle X0Y is 90 o, and angle 0XY is 60 o, what is angle 0YX?

11
Review of Trig Sine = ord/hyp Cos = abs/hyp Tan = ord/abs P4 If = 60 o and hyp = 2 meters how long is the ordinate? Hint: We know the hypotenuse and the angle, so we can look up the sine. We want the ordinate. The sine = ord/hyp, so we can solve for the ordinate.

12
Review of Trig Sine = ord/hyp (1) Cos = abs/hyp (2) Tan = ord/abs (3) P4 If = 60 o and hyp = 2 meters how long is the ordinate? Hint: We know the hypotenuse and the angle, so we can look up the sine. We want the ordinate. The sine = ord/hyp, so we can solve for the ordinate. Soln: Sine 60 o = 0.866 Solve Eqn (1) for ordinate ordinate = Sine * hypotenuse Plug in: ordinate = 0.866 * 2 meters ordinate = 1.732 meters

Similar presentations

OK

Right Triangle Trigonometry Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 The six trigonometric functions of a.

Right Triangle Trigonometry Digital Lesson. Copyright © by Houghton Mifflin Company, Inc. All rights reserved. 2 The six trigonometric functions of a.

© 2017 SlidePlayer.com Inc.

All rights reserved.

Ads by Google

Ppt on life of gautama buddha Ppt online open school Retinal anatomy and physiology ppt on cells Ppt on septic abortion Ppt on power generation by speed breakers What does appt only means you love Ppt on index numbers in economics Ppt on domestic robots Ppt on video teleconferencing installation Ppt on intelligent manufacturing wikipedia