Intro Hi class! Welcome back to our channel. For this video, we will discuss angle measure.
An angle is formed by rotating a ray about its endpoint. Okay, so in the figure shown below, Ang initial side ng ating angle AOB is yung side OA. Then yung ating terminal side is yung side OB.
Nakuha? So sa given angle guys, yung terminal side yung nagro-rotate. Then, pagka ang rotation ng ating terminal side is counterclockwise, ang measurement ng ating angle is positive. Then, pagka ang rotation naman ng ating terminal side is clockwise, ang measurement ng ating angle is negative.
Okay? So, next is the angles in standard position. So, sabi dito, an angle is in standard position. If it is drawn in the Cartesian plane with its vertex at the origin and its initial side on the positive x-axis.
So as you can see guys, dito sa tatlong angles natin, yung angle alpha, yung kanyang initial side is na kay positive x-axis. Dama? Then yung vertex ng ating angles is nasa...
Origin. So that means, si angle alpha, angle theta, and angle beta is in standard position. Nakuha? So ngayon, since si a and theta, si alpha and theta is nag-rotate ng counterclockwise, so that means, yung measurement nila is parehas positive. Tama.
Then, si angle beta, since nag-rotate ng clockwise, ang measurement nito guys is negative. Nakuha? So, next is yung kanilang measurement.
Pagka ang angle natin guys is naka graph sa ating Cartesian plane, maaari natin makuha yung kanilang measurement. Okay? So pagka ang angle natin tumapat, yung terminal side natin tumapat dito kay positive x-axis, ang kanyang measurement is 0 degrees. Nakuha?
Then pagka nag-move tayo, papunta kay y, ang measurement nya na guys is 90 degrees. Then, papunta dito kay negative x-axis, we have 180 degrees. Then, dito naman sa may baba, that is 270 degrees. Okay? So, yan yung measurement kapagka ang ikot ng ating angles is counterclockwise.
So, pagka naka isang revolution tayo guys, that is equivalent to 360 degrees. Okay? So, what if naman kung...
clockwise yung rotate ng ating terminal side. So sa unang rotate nya, papunta dito sa may baba, ang measurement nyan guys is negative 90 degrees. Okay?
Then dito naman sa may negative x-axis, this is negative 180 degrees. Then sa taas, we have negative 270 degrees. Then ang isang revolution, we have negative 360 degrees. Nakuha?
So ngayon, ibig sabihin, pagka ang angle natin, o yung terminal side natin, is nasa kwadrant 1, ang measurement ng ating angle is between 0 degrees to 90 degrees. Okay? Sa may kwadrant 2 naman, yung measurement ng angle natin is between 90 degrees to 180 degrees. Then for quadrant 3, ang measurement ng ating angle we have is between 180 and 270. Then for quadrant 4, ang measurement naman ng ating angle is between 270 degrees up to 360 degrees.
Okay? So, let's have our first example. So, find the measure of each angle. So, dito guys, ang pinapakuha is yung measurement ng ating angle na nag-rotate yung kanyang terminal side counterclockwise.
Okay, so ibig sabihin, ang measurement ng ating angle is positive. Okay, so ang given natin dito is yung 80 degrees. Dito guys, simula sa ating negative y-axis going to our terminal side. So kung 80 yan, ibig sabihin, yung remaining dito guys is 10 degrees. Tama?
So, yun nga lang, ang pinapakuwang measurement dito guys is yung nag-rotate ng counterclockwise. Tama? So, ibig sabihin, para makuha natin yung measurement na yan, ima-minus natin yung 10 degrees kay 360 degrees.
Tama? So, since ang isang revolution ng ating terminal side is 360, so, bawasan lang natin ng 10 kasi may iniwan tayong 10 degrees dito. So, ibig sabihin, ang measurement ng ating angle is 350 degrees.
Okay? So, next, number 2. So, this time, yung ating terminal side is nag-rotate ng clockwise. So, that means, yung ating terminal side is negative.
Tama? So, kung ang given dito guys is yung 20 degrees. So, ibig sabihin, yung naiwan dito, we have 70 degrees.
Okay, so ngayon, alam naman natin na yung half revolution ng ating terminal side measures 180 degrees. Tama? Yung kalahati. So i-add natin ngayon itong 70 degrees. So 180 plus 70, that is 250 degrees.
But since nag-rotate yung ating terminal side ng counterclockwise, base, And, ng clockwise, so, ibig sabihin, yung measurement natin is negative. Okay? So, last, number 3. We have...
Positive angle since nag-rotate yung ating terminal side ng counterclockwise. So, that means positive. Tama?
So, ang given natin dito guys is yung 170. So, pwede nating malaman ang measurement na tira dito is 10 degrees. Okay? So, kung i-observe natin guys yung rotation ng ating terminal side, nag-rotate yung ating terminal side guys ng isang ikot. Tama, na isang revolution. So, ibig sabihin, naka 360 degrees na siya.
Tapos ngayon, nag-add pa tayo ng konti, ng 10 degrees. So, i-add natin ngayon yan dito. Then, ang total measurement ng ating angle is now 370 degrees.
Naintindihan guys? So, let's proceed now to another example. So this time, we are asked to draw an angle with the given measure in standard position, then state the quadrant in which the terminal side of each angle lies.
So una, ang given angle natin is 280 degrees. So since positive, ibig sabihin ang rotation ng ating angle is counterclockwise. Tama?
So since the angle is in standard position, So, ibig sabihin, dito tayo mag-i-start guys kay positive x-axis. Ito yung ating initial side. Then, yung ating vertex is dapat na kay origin.
Okay? So, 280 degrees. So, bilang tayo.
So, una, we have 0 degrees, 90 degrees, 180, then 270 degrees. Okay? So, since umabot tayo kay 270, then 280 ang kailangan natin. Since wala naman tayong protractor, so i-estimate na lang natin yung 10 degrees. Okay?
So, from 270 guys, mag-a-add lang tayo ng siguro at least 10 degrees. Estimate na lang natin. So, ito ngayon guys yung ating 280 degrees. Okay, so ngayon after natin ma-sketch yung ating angle, state naman natin anong kwadran sya yung ating terminal side huminto. So as you can see, nasa kwadran 4 tayo.
Okay, so next we have negative 120. 20 degrees. So, kung negative yung ating angle, so that means yung ating rotation is clockwise. Okay? So, ito yung ating 0 degrees. Then, we have negative 90 degrees.
Then, negative 180 degrees. So, standard position, yung ating initial side is nandito sa ating positive x-axis. Okay? So, since negative, again, Clockwise yung ating rotation. Okay?
So, kung negative 120 yung measurement ng ating angle, ibig sabihin, hindi tayo aabot, or hindi na tayo lalagpas doon kay 180. So, from negative 90, so estimate natin yung 30. Okay? So, somewhere yan dito magpo-fall. So, these measures guys, ito yung ating negative 120 degree na yung ating terminal side is nasa quadrant 3. Okay?
So, next we have 710 degrees. Okay? So, alam naman natin ang isang rotation ng ating terminal side, it measures 360. Tama, so ibig sabihin lalagpas tayo ngayon sa isang ikot. Okay, so try natin.
So ibig sabihin kung nag-rotate yung ating terminal side ng isang ikot, pwede na tayo mag-minus ng 360 dito sa ating given angle. Okay, so 710 minus 360 yung isang rotation. So ang kulang na lang natin is 350. Okay, so kung 350 yan, ibig sabihin, halos magdadalawang ikot na yan, then pwede tayong mag-estimate na lang dito, magtira tayo ng 10 degrees.
Dun sa may kabila. So yung 350 guys, dito na yan magpa-fall. Okay, so ito na ngayon guys yung ating 710 degrees na makikita yung terminal side in quadrant 4. Okay, next.
Last example, we have 440 degrees. So same procedure tayo din sa pangatlong example natin. Isang ikot muna tayo yun ng ating terminal side.
So after natin mag isang ikot, magma minus 360 tayo. So ang kulang na lang natin guys is 80 degrees. Okay?
So kung ang positive y-axis natin it measures 90 degrees, ibig sabihin hindi na tayo lalagpas dun. Tama? So, magbawas na lang tayo guys ng 10 degrees from 90 degrees.
So, estimate natin, nandito yan. Okay? So, dyan tayo hihinto.
So, ito ngayon guys yung ating 440 degrees na yung terminal side is nasa kwadrant 1. Okay? So, again guys, lahat ng measurement natin dito is inestimate lang natin. Kung gusto nyo mas accurate yung inyong mga sketch or yung mga draw, make sure na gumamit kayo ng protractor.
Okay? So, this is the end of our video. I hope naintindihan nyo guys kung paano ba mag-sketch ng angles and paano ba makuha yung mga different measurement ng ating angles.
So, if you have questions or clarifications, kindly put them in the comment section below. Thank you guys for watching. This is Prof. D. I'll catch you on the flip side.
Bye! Music