Triangles on the Cartesian Plane - Ms Beaubien's Classroom

Warm-Up: Applications of Right Triangles At ground level, the angle of elevation to the top of a building is 78. If the measurement is taken 40m from the base of the building, determine the height of the building. Lesson 3:Triangles on the Cartesian Plane

LG: I can determine the measure of an angle in standard position on a Cartesian plane. I can determine the values of the sine, cosine and tangent of obtuse angles. Angle Terms Acute Angle = less than 90 Obtuse Angle = Greater than 90 (but less than 180) Reflex Angle = greater than 180

Supplementary Angles = two angles that add to 180 two right angles, or One acute and one obtuse angle obtuse acute Angle Conventions On a Cartesian plane (or co-ordinate axes) we position angles like this: Terminal arm

Positive angles are read counter-clockwise Rotation Angle Initial arm Angles are said to be in standard position when the vertex is at the origin (0,0) and the initial arm is located on the positive x-axis

Calculator Practice Determine the sine, cosine and tangent for each angle. a) 115o b) 100o Is each trigonometric ratio positive or negative? Use a calculator to verify. a) sin98o b) tan134o Determine the measure of angle R for the cosine ratio -0.75.

Triangles on a Cartesian Plane Given the point (x, y), we know 2 side lengths of the right triangle Pythagorean theorem could be used to solve for the hypotenuse (r) Knowing all three sides of the triangle, we can use any primary trig ratio (sin, cos, or tan) to determine the measure of angle

r EXAMPLE 1 Acute Angles in Standard Position For the angle in standard position with a terminal arm passing through P(5, 2): a) Find the length of r

b) Determine the measure of each trig ratio. Round your answers to four decimal places. c) Determine the measure of to the nearest whole angle. EXAMPLE 2 Obtuse Angles in Standard Position The point P( 3, 7) lies on the terminal arm of an angle, , in standard position. Calculate to the nearest whole degree.

Practice Pg. 23 #1, 2, 4-7

Recently Viewed Presentations

  • IPS Software Systems - International Perforating Forum

    IPS Software Systems - International Perforating Forum

    2015 International Perforating Symposium The Renaissance Hotel, AmsterdamTuesday thru Thursday, May 19-21, ... Guns and firing system internals "disappear" toallow unrestricted flow of production without pulling guns. ... IPS Software Systems
  • Unit 4: Hair

    Unit 4: Hair

    Cuticle. Cortex. Medulla. Objective: SWBAT identify forensic evidence found in hair samples. Objective: SWBAT identify forensic evidence found in hair samples. The cuticle is the outside covering made of overlapping scales. Scales point down towards tip (older part) of hair.
  • Family Care

    Family Care

    Case study. Patient: 86 year old man found down at home by his wife for an unknown amount of time.EMS did CPR and got a pulse. They transported him to the hospital where he coded and was worked on for...
  • Solving two-player zero-sum extensive-form games

    Solving two-player zero-sum extensive-form games

    Plan for next part of the presentation. We will introduce counterfactual regret minimization (CFR)-based equilibrium finding in two-player zero-sum games. Most common algorithm. Relatively easy to understand and implement. We start from first principles and proceed step by step to...
  • ATMS 316- Mesoscale Meteorology  Packet#6  Interesting things happen

    ATMS 316- Mesoscale Meteorology Packet#6 Interesting things happen

    Frontal gradients that appear discontinuous from those of the synoptic-scale background. Relative minimum in pressure. Relative maximum of vorticity along the front. Zone of confluence along the front. Strong vertical and lateral (cyclonic) wind shear. Rapid changes in cloud cover...
  • Pro Forma Financial Statements - WordPress.com

    Pro Forma Financial Statements - WordPress.com

    The sender's address The senders mailing address Phone number and e-mail address Date being sent Heading 234 South 3rd Street Drew, MS 38737 June 6, 2001 Inside Address The inside address gives the name and address of the person or...
  • Dementia Awareness

    Dementia Awareness

    INTERDEM. INTERDEM is a pan-European network of researchers collaborating in research on and dissemination of Early, Timely and Quality Psychosocial Interventions in Dementia aimed at improving the quality of life of people with dementia and their supporters, across Europe.. so...
  • Projectile Motion Problems - Uplift Education

    Projectile Motion Problems - Uplift Education

    To solve projectile motion problems, you must separate the horizontal and vertical components of motion. ... A rock is thrown from a 50.0 m high cliff with an initial velocity of 7.0 m/s at an angle of 53o above the...