Presentation is loading. Please wait.

Presentation is loading. Please wait.

Gebze Institute of Technology Department of Architecture

Published byDaisy Parks Modified over 7 years ago

Similar presentations

Presentation on theme: "Gebze Institute of Technology Department of Architecture"— Presentation transcript:

1 Gebze Institute of Technology Department of Architecture
MAT119 Asst. Prof. Ferhat PAKDAMAR (Civil Engineer) M Blok - M106 Fall – 2014 Week 9

2 Right Triangles and Vectors
Pythagorean Theorem Pythagorean Triples Special Triangles Trigonometric Functions and Special Angles Trigonometric Function Values in Quadrants II, III, IV Graphs of Trigonometric Functions Vectors, Operating with Vectors

3 Vectors

4 Vectors

5 Addition of Vectors 𝑠𝑖𝑛𝐴 𝑄 = 𝑠𝑖𝑛𝐵 𝑅 = 𝑠𝑖𝑛𝐶 𝑃

6 Addition of Vectors cnt’d

7 Sample (adding vectors)

8 Sample (adding vectors) cnt’d

9 Sample (adding vectors) cnt’d

10 Unit Vectors

11 Addition of vectors by summing Components

12 Sample (adding vectors by summing components)

13 Sample (adding vectors by summing components) cnt’d

14 Rectengular Components in Space

15 Rectengular Components in Space ctn’d

16 Rectengular Components in Space ctn’d

17 Sample

18 Sample cnt’d

19 Sample cnt’d

20 Thank You

Download ppt "Gebze Institute of Technology Department of Architecture"

Similar presentations

Special Right Triangles

Special Right Triangles
Pythagoras Bingo. Pick 8 from the list 8920 90C 5101520 965no 16124yes Pythagorean triple Hypotenuse Pythagoras theorem.

Pythagoras Bingo. Pick 8 from the list C no 16124yes Pythagorean triple Hypotenuse Pythagoras theorem.
The Pythagorean Theorem leg hypotenuse leg Applies to Right Triangles only! The side opposite the right angle The sides creating the right angle are called.

The Pythagorean Theorem leg hypotenuse leg Applies to Right Triangles only! The side opposite the right angle The sides creating the right angle are called.
Section 14-4 Right Triangles and Function Values.

Section 14-4 Right Triangles and Function Values.
MAT120 Asst. Prof. Dr. Ferhat PAKDAMAR (Civil Engineer) M Blok - M106 Gebze Technical University Department of Architecture Spring.

MAT120 Asst. Prof. Dr. Ferhat PAKDAMAR (Civil Engineer) M Blok - M106 Gebze Technical University Department of Architecture Spring.
1.5 Using the Definitions of the Trigonometric Functions OBJ: Give the signs of the six trigonometric functions for a given angle OBJ: Identify the quadrant.

1.5 Using the Definitions of the Trigonometric Functions OBJ: Give the signs of the six trigonometric functions for a given angle OBJ: Identify the quadrant.
1 1 1 2 *Special Angles 45° 60° 30° 30°, 45°, and 60° → common reference angles Memorize their trigonometric functions. Use the Pythagorean Theorem;

*Special Angles 45° 60° 30° 30°, 45°, and 60° → common reference angles Memorize their trigonometric functions. Use the Pythagorean Theorem;
March 2 nd copyright2009merrydavidson HAPPY BIRTHDAY TO: Khalil Nanji.

March 2 nd copyright2009merrydavidson HAPPY BIRTHDAY TO: Khalil Nanji.
UNIT 2 Two Dimensional Motion

UNIT 2 Two Dimensional Motion
Unit 37 VECTORS. DEFINITIONS A vector is a quantity that has both magnitude and direction Vectors are shown as directed line segments. The length of the.

Unit 37 VECTORS. DEFINITIONS A vector is a quantity that has both magnitude and direction Vectors are shown as directed line segments. The length of the.
I.1 ii.2 iii.3 iv.4 1+1=. i.1 ii.2 iii.3 iv.4 1+1=

I.1 ii.2 iii.3 iv.4 1+1=. i.1 ii.2 iii.3 iv.4 1+1=
The Pythagorean Theorem From The Simpson’s Homer copies the Scarecrow on The Wizard of Oz.

The Pythagorean Theorem From The Simpson’s Homer copies the Scarecrow on The Wizard of Oz.
I.1 ii.2 iii.3 iv.4 1+1=. i.1 ii.2 iii.3 iv.4 1+1=

I.1 ii.2 iii.3 iv.4 1+1=. i.1 ii.2 iii.3 iv.4 1+1=
Solving Right Triangles Given certain measures in a right triangle, we often want to find the other angle and side measures. This is called solving the.

Solving Right Triangles Given certain measures in a right triangle, we often want to find the other angle and side measures. This is called solving the.
The Pythagorean Theorem. The Right Triangle A right triangle is a triangle that contains one right angle. A right angle is 90 o Right Angle.

The Pythagorean Theorem. The Right Triangle A right triangle is a triangle that contains one right angle. A right angle is 90 o Right Angle.
MAT120 Asst. Prof. Ferhat PAKDAMAR (Civil Engineer) M Blok - M106 Gebze Technical University Department of Architecture Spring – 2014/2015.

MAT120 Asst. Prof. Ferhat PAKDAMAR (Civil Engineer) M Blok - M106 Gebze Technical University Department of Architecture Spring – 2014/2015.
Lesson 10.1 The Pythagorean Theorem. The side opposite the right angle is called the hypotenuse. The other two sides are called legs. We use ‘a’ and ‘b’

Lesson 10.1 The Pythagorean Theorem. The side opposite the right angle is called the hypotenuse. The other two sides are called legs. We use ‘a’ and ‘b’
Objective: Find the components of a vector.. Number plane, or Cartesian coordinate system – a plane determined by the horizontal line called the x- axis.

Objective: Find the components of a vector.. Number plane, or Cartesian coordinate system – a plane determined by the horizontal line called the x- axis.
Benchmark 40 I can find the missing side of a right triangle using the Pythagorean Theorem.

Benchmark 40 I can find the missing side of a right triangle using the Pythagorean Theorem.
MA.912.T.2.1 CHAPTER 9: RIGHT TRIANGLES AND TRIGONOMETRY.

MA.912.T.2.1 CHAPTER 9: RIGHT TRIANGLES AND TRIGONOMETRY.

Similar presentations

Ads by Google