This document discusses trigonometry and introduces Hipparchus of Bithynia as the Greek mathematician who systematized trigonometry. It defines the trigonometric functions of sine, cosine, and tangent using the mnemonic SOH-CAH-TOA. It also defines angle of elevation and angle of depression and provides examples of calculating trigonometric functions in right triangles. Finally, it gives an assignment involving using trigonometric functions to find the height of a hot air balloon.

1. Who am I? I was credited for preparing tables of sines used for solving problems in astronomy and a Greek mathematician of antiquity introduced trigonometry as a systematized body of knowledge. “ I am the eight letter of the alphabet + the symbol of the imaginary number + double the first letter of polynomial + (3a-2a) +r + c + the inverse of “n” + 20 th letter-1”

2. YES, I am Hipparcus of Bithynia (190-120 B.C.)

3. Welcome to the world of mathematics Area of specialization Trigonometry

4. One common mnemonic is to remember the SOH-CAH-TOA. In this lesson, we will consider the sine, cosine and tangent functions and the meaning of the two angle namely: the angle of elevation and depression respectively. Now you know the person behind trigonometry let us now explore his works.

5. Let us consider this right triangle. What have you observed?

6. The side opposite the right angle is the hypotenuse. The sides opposite the two acute angles are legs called opposite and adjacent of angle t .

7. But our problem here is to solve for the unknown angle or the theta “ θ ”. Now we can apply the mnemonic that we have, the famous SOH-CAH-TOA.

8. The sine of an angle is the ratio of the opposite side to the hypotenuse side. SOH opposite hypotenuse

9. Example: Calculate the value of sin θ in the following triangle. Solution:

10. The cosine of an angle is the ratio of the adjacent side and hypotenuse side. CAH adjacent hypotenuse

11. Example: Calculate the value of cos θ in the following triangle. Solution:

12. The tangent of an angle is the ratio of the opposite side and adjacent side. TOA opposite adjacent

13. Example: Calculate the value of tan θ in the following triangle. Solution:

14. Application P a.) 21 b.) 53 20 t M 29 45 Find the values of the three trigonometric functions (soh, cah, toa) for each of the following indicated angles.

15. Activity 2

16. The two angles Angle of Elevation The word “elevation” means “rise” or “move up”. Angle of elevation is the angle between the horizontal and the line of sight to an object above the horizontal. Angle of Depression The word “depression” means “fall” or “drop”. Angle of depression is the angle between the horizontal and the line of sight to an object beneath the horizontal.

17. Take a look at the example below. In the picture below, an observer is standing at the top of a building and looking straight ahead at the birds (horizontal line). The observer must raise his eyes to see the airplane (slanting line). The angle formed between the two lines is called the angle of elevation.

18. Take a look at the example below. In the picture below, an observer is standing at the top of a building and looking straight ahead at the birds (horizontal line). The observer must lower his eyes to see the car parked (slanting line). The angle formed between the two lines is called the angle of depression.

19. Assignment Find the height of a hot air balloon which is directly above a nipa hut if the angle of depression of a carabao, 62 m away from the nipa hut is 14 º55’. Note: Use the possible trigonometric function/s in answering your assignment.

20. Study your lessons. Don’t give up! I know you can do it.