1. Day 3 – Basic Concepts Objectives: At the end of the period, I should be able to... Define Trigonometry Review the concept of an angle Identify the rotation of an angle given the sign of its measure

2. Essential Questions I will find the answer to the questions… 1. What is the best way to solve the missing parts of a triangle? 2. How can we solve real-life problems using trigonometric function and how?

3. Definition of Trigonometry TRIGONOMETRY “Trigonon” “Metron”

4. Definition of Trigonometry Open your MLDs and go to your respective link:  10-E: http://padlet.com/jose_calamlam/qkyz 1aycxlrf Answer the question “What is Trigonometry”. Write your group number in the title (red) and then your answer in the body (black).

5. Definition of Trigonometry “Trigonometry is a branch of mathematics that studies relationships involving sides and angles of triangles”.

6. Question # 1 What is an angle? ____________________ How is it formed? _____________________

7. ANGLE It is formed by rotating a ray around its endpoint. The ray in its initial position is called the initial side of the angle, while the ray after the rotation is the terminal side of the angle. The endpoint of the ray is the vertex of the angle.

8. Question # 2 When is an angle in standard position? Give the two conditions for an angle to be in standard position. 1.________________________________ 2. ________________________________

9. When the vertex of an angle is the origin of the coordinate plane and its initial side coincides with the positive x – axis, the angle is said to be in standard position. Initial side Terminal side Vertex x - axis y - axis

10. Open TRIG WIZARD Set the initial ray at 0 Click the + button on the bottom left Click the - button on the bottom left Stop the rotation by pressing the same button

11. Question # 3 Complete the statements:  If the terminal side is rotating counter clockwise, then the angle formed is ____________________  If the terminal side is rotating clockwise, then the angle formed is ____________________

12. If the rotation of the terminal side is counterclockwise, the angle is positive. If the rotation is clockwise, the angle is negative. Positive angle Negative angle

13. How many degrees is one complete or full counter clockwise rotation? One unit of angle measure is the degree. One full counterclockwise rotation measures 360 0, and one full clockwise rotation measures - 360 0. Question # 4

14. Example # 1: How many degrees is 2/3 rotation clockwise? If it is in standard position, in which quadrant does its terminal side lie? Solution: = 2 ( - 120 0 )= - 240 0 - 240 0 + 360 = 120 0 QII Example # 2: How many degrees is 15/24 rotation counterclockwise? If it is in standard position, in which quadrant does its terminal side lie?

15. Open TRIG WIZARD Given angle is inscribed in the cartesian plane, observe the measures of the angles when it’s terminal side is in … Quadrant I Quadrant II Quadrant III Quadrant IV

16. If an angle lies in the coordinate plane, what are the measures of the angles in QI? QII? QIII? QIV? QI = between 0 0 to 90 0. QII = between 90 0 to 180 0. QIII = between 180 0 to 270 0. QIV = between 270 0 to 360 0. Question # 5

17. What are coterminal angles? Question # 6

18. Coterminal angles are angles in standard position whose terminal sides coincide. Example # 3: Sketch 60 0 and 420 0 in the coordinate plane and identify if they are coterminal angles. 60 0 360 0

19. How does one find an angle which is coterminal with the given angle or a given condition? Question # 7

20. By adding or subtracting integral multiples of 360 0. Example # 4: Are – 110 0 and – 830 0 coterminal angles? Why?

21. Questions 1.Convert 30° to radian measure. 2.Convert π/3 rad to degree measure. Instructions: 1.Write your answers with solution in a one whole sheet of pad paper. 2.Take a picture of your paper. 3.Submit the picture in your Google Classroom. Homework 1

22. Refer to these links: Degree  Radian: https://www.khanacademy.org/math/trigonometry/unit- circle-trig-func/radians_tutorial/v/we-converting-degrees-to- radians Radian  Degree: https://www.khanacademy.org/math/trigonometry/unit- circle-trig-func/radians_tutorial/v/we-converting-radians-to- degrees Extra examples: https://www.khanacademy.org/math/trigonometry/unit- circle-trig-func/radians_tutorial/v/radian-and-degree- conversion-practice Homework 1