Day 3 – Basic ConceptsObjectives: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

Essential QuestionsI 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?

Definition of Trigonometry

TRIGONOMETRY

“Trigonon” “Metron”

Definition of Trigonometry• Open your MLDs and go to your respective

link: 10-E: http://padlet.com/jose_calamlam/qkyz1aycxlrf

• Answer the question “What is Trigonometry”.• Write your group number in the title (red) and

then your answer in the body (black).

Definition of Trigonometry

“Trigonometry is a branch of mathematics that studies

relationships involving sides and angles of triangles”.

Question # 1

What is an angle? ____________________

How is it formed? _____________________

• 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.

Question # 2

When is an angle in standard position?

Give the two conditions for an angle to be in standard position.1. ________________________________2. ________________________________

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

Vertexx - axis

y - axis

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

Question # 3Complete 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 ____________________

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

How many degrees is one complete or full counter clockwise rotation?

One unit of angle measure is the degree. One full counterclockwise rotation measures 3600 , and one full clockwise rotation measures

- 3600.

Question # 4

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 ( - 1200) = - 2400

- 2400 + 360 = 1200 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?

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 IQuadrant IIQuadrant IIIQuadrant IV

If an angle lies in the coordinate plane, what are the measures of the angles in QI? QII? QIII? QIV?

QI = between 00 to 900.

QII = between 900 to 1800.

QIII = between 1800 to 2700.

QIV = between 2700 to 3600.

Question # 5

What are coterminal angles?

Question # 6

Coterminal angles are angles in standard position whose terminal sides coincide.

Example # 3: Sketch 600 and 4200 in the coordinate plane and identify if they are coterminal angles.

600

3600

How does one find an angle which is coterminal with the given angle or a given condition?

Question # 7

By adding or subtracting integral multiples of 3600 .

Example # 4: Are – 1100 and – 8300 coterminal angles? Why?

Questions1. Convert 30° to radian measure.2. Convert π/3 rad to degree measure.

Instructions:3. Write your answers with solution in a one whole sheet of

pad paper.4. Take a picture of your paper.5. Submit the picture in your Google Classroom.

Homework 1

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