Understanding Trigonometry in Taglish: Lesson 6 - Converting Degrees to Radians and Vice Versa

 LESSON 6 – Converting DEGREE to RADIAN and vice versa

Matapos nating mapag-aralan ang mga uri ng linya, salikop o anggulo, trianggulo, complementary at supplementary angles, gayundin ang katuturan ng Pythagorean Theorem, sa leksyon 6 ay susubukin naman nating lubos na maunawaan ang degree at radian.

Sa araling ito, malalaman mo ang pagkakaiba sa pagitan ng dalawang yunit ng pagsukat na ginamit para sa mga anggulo: degree at radian. Malalaman mo rin kung paano i-convert ang isang unit sa isa pa.

Ang araling ito ay mahalaga sapagkat may mga problema na maaaring matugunan mo sa hinaharap na nagsasangkot ng pagsukat ng mga anggulo.

Pagmasdan ang bilog sa ibaba:

CIRCUMFERENCE = the yellow ring

The circumference is the distance around a circle. It is always equal to 360 unit (either  degree (o) or radian (rad)).

A degree is a unit of measurement equal to 1/360 of the circumference of a circle. 

From this, we can conclude that:

     90^o = 90 (1/360) of the circumference = ¼ of the circumference 

   180^o = 180 (1/360) of the circumference = ½ of the circumference 

   270^o = 270 (1/360) of the circumference = ¾ of the circumference

The circumference of a circle = 2π (2 pi). (pi is pronounced as “pie”)

π (pi) = is a symbol that has a constant value. Ito ay katumbas ng 3.1416 o ≈ 3.1416 na nakuha matapos i-divide ang circumference sa 2 radius (o diameter).

 Hindi eksakto ang value ng pi kaya ginagamit ang simbolong ≈, na ang ibig sabihin ay “approximate”. 

There are π/180^o or 0.01745 rad in 1°. So, to convert degrees to radians, we multiply the number of degrees by π/180^o or 0.01745 rad. 

 

Ang isang degree ay may katumbas na π/180^o o  0.01745 rad. Kung gayon, para ma-convert ang value ng degree sa radian, i-multiply lamang ang degree sa π/180^o  o  0.01745 rad..

Mga Halimbawa

Convert the following degrees into radians.

1. 30^o  = 30^o (π/180^o) = 3π/18 = π/6 rad

2. 90^o  = 90^o (π/180^o) = 9π/18 = π/2 rad

3. 225^o  = 225^o (π/180^o) = 45π/36 = 5π/4 rad

4.  74^o = 74^o (0.01745) = 1.2913 rad

5. 300^o = 300^o (0.01745) = 5.235 rad

There are 180^o/π or 57.2956^o  in 1 rad. Thus, to convert radians to degrees, we multiply the number of radians by 180^o/π or 57.2956°.

 

Ang isang radian o 1 rad ay may katumbas na 180^o/π  o  57.2956 degrees. Kung gayon, para ma-convert ang value ng radian sa degree, i-multiply lamang ang radian sa 180^o/π  o  57.2956^o.

Mga Halimbawa

Convert the following radians into degrees.

1. 3π/4 rad = 3π/4 (180^o/π) = 540/4 = 135^o

2. 5π/3 rad = 5π/3 (180^o/π) = 900/3 = 300^o

3. 11π/6 rad = 11π/6 (180^o/π) = 1980/6 = 330^o

4. 0.6 rad = 0.6 (57.2956^o) = 34.3774^o

5. 2π rad =  2 (3.1416) (57.2956^o) = 360^o

Tandaan

1. A degree is equal to 1/360 of the circumference of a circle.

2. A radian, if placed at the center of a circle, makes an arc equal to the radius of the circle.

3. p180° rad or .01745 rad = 1°

4. To convert degrees to radians, we multiply the number of degrees by π/180° or  0.01745.

5. 180°/p or 57.2956° = 1 rad.

 6. To convert radians to degrees, we multiply the number of radians by 180°/π or 57.2956°.

A pi (π) has an approximate value of 3.1416  or 22/7.  π =  circumference/diameter of a circle

Understanding Trigonometry in Taglish: Lesson 4 - SOLVING REAL-LIFE PROBLEMS USING THE PYTHAGOREAN THEOREM

 LESSON 4 – SOLVING REAL-LIFE PROBLEMS USING THE PYTHAGOREAN THEOREM

Matapos nating mapag-aralan ang mga uri ng linya, salikop o anggulo, complementary at supplementary angle gayundin ang katuturan ng Pythagorean Theorem, sa leksyon 4 ay susubukin naman nating mabigyang solusyon ang mga halimbawa ng mga problema sa tunay na buhay gamit ang bisa ng Pythagorean Theorem ni Pythagoras.

Dapat lamang nating tandaan na ang Pythagorean Theorem ay ginagamit lamang kung may mabubuo tayong right angle o right triangle.

STEPS in solving problems involving RIGHT TRIANGLES:

Nasa ibaba ang mga hakbang upang masolusyonan ang isang Math problem na kinassangkutan ng Right Triangle:

STEP 1 Identify the hypotenuse and the legs of the triangle. (Tukuyin ang hypotenuse at mga legs ng triangle.)

STEP 2 Use the formula derived from the Pythagorean theorem. (Gamitin ang formula ng Pythagorean theorem: c2 = a2 + b2)

STEP 3 Substitute the given values to the variables in the formula and solve for the unknown. (Ilagay ang mga values na ibinigay sa problema at hanapin ang unknown.)

STEP 4 Simplify to get the final answer. (Gawing simple ang sagot)

[Problem 1 to 4 from ALS Junior High School Module Trigonometric Functions 1]

Problem 1

Jake was performing his favorite billiard trick shot. He hit the cue ball and it went to one corner of the table, rolled to the other corner, hit the exact center of the back cushion and hit the eighth ball causing it to drop into one of the holes before returning to its original position. If the dimensions of the table are 6 ft. by 8 ft., how far did the cue ball travel?

Problem 2

Alice, a landscape architect, designed a flowerbed for a very important client. The flowerbed will take the shape of a right triangle with legs equal to 12 ft. and 9 ft. She wants to place some decorative stones along the hypotenuse of the flowerbed 1 ft. apart. How many stones does she need?

Problem 3

Two cars start traveling perpendicularly away from each other from the same place. If one travels 6 km and the other 8 km, how far apart will they be from each other using their bumpers as points of reference? 

Problem 4

A pendulum travelled 30 cm away from a center line. The center line is 40 cm long. What is the distance between the pendulum and one end of the center line?

Problem 5

A ladder 13 m long is placed on the ground in such a way that it touches the top of a vertical wall 12 m high. Find the distance of the foot of the ladder from the bottom of the wall. 

(Source: https://www.math-only-math.com)

TANDAAN

1. Magagamit lamang ang Pythagorean Theorem sa  mga right angles o right triangles.

2. Hindi lang sukat ng hypotenuse ang mahahanap sa Pythagorean Theorem kundi maging ang iba pang sukat/haba ng mga sides/legs (opposite and adjacent sides) kung ang 2 sukat ay ibinigay.

3. Mag-drawing kung hindi ma-imagine ang larawang isinasaad ng problem.

4. Tandaan ang square root ng ilang bilang tulad ng:

1 = square root ng 1 dahil 1 x 1 or 1² = 1

2 = square root ng 4 dahil 2 x 2 or 2² = 4

3 = square root ng 9 dahil 3 x 3 or 3² = 9

4 = square root ng 16 dahil 4 x 4 or 4² = 16

5 = square root ng 25 dahil 5 x 5 or 5² = 25

6 = square root ng 36 dahil 6 x 6 or 6² = 36

        7 = square root ng 49 dahil 7 x 7 or 7² = 49

8 = square root ng 64 dahil 8 x 8 or 8² = 64

9 = square root ng 81 dahil 9 x 9 or 9² = 81

10 = square root ng 100 dahil 10 x 10 or 10² = 100

11 = square root ng 121 dahil 11 x 11 or 11² = 121

12 = square root ng 144 dahil 12 x 12 or 12² = 144

13 = square root ng 169 dahil 13 x 13 or 13² = 169

14 = square root ng 196 dahil 14 x 14 or 14² = 196

15 = square root ng 225 dahil 15 x 15 or 15² = 225

Alalahanin na ang 

A = square root ng Y dahil A x A (A times A) or A² = Y

A square root of a number (Y) is one of the factors (A)  of Y such that when you multiply it TWO (2) times (A x A) or you square it (A²), you will get that number Y.