CLASS 10TH DAY 6
INTRODUCTION
Trigonometric Ratios Of some specific angles
Before we move further, we hope you have solved at least till exercise 8.1 of ncert class 10th. If not, please solve before you move further.
So today we are going to study trigonometric ratios of some specific angles which are 0, 30, 45, 60, 90. These angles are very commonly used and we need to remember these angles too.
Trigonometric Ratio of 45°:
If an acute angle of a right triangle is 45°, then the other acute angle is also 45°.
Thus the triangle is isosceles. Let us consider the triangle ABC with
∠B = 90°
∠A = ∠C = 45°
Then AB = BC.
Let AB = BC = a.
By Pythagorean theorem,
AC2 = AB2 + BC2
AC2 = a2 + a2
AC2 = 2a2
Take square root on each side.
AC = a√2
Hence, we can find the trigonometric ratios of angle 45° from the right triangle ABC.
Trigonometric Ratios of 30° and 60°:
Let ABC be an equilateral triangle whose sides have length a (see the figure given below). Draw AD perpendicular to BC, then D bisects the side BC. Then,
BD = DC = a/2
∠BAD = ∠DAC = 30°
Now, in right triangle ADB, ∠BAD = 30° and BD = a/2. In right triangle ADB, by Pythagorean theorem,
AB2 = AD2 + BD2
a2 = AD2 + (a/2)2
a2 – (a2/4) = AD2
3a²/4 = AD2
√(3a2/4) = AD
√3 ⋅ a/2 = m AD
Hence, we can find the trigonometric ratios of angle 30° from the right triangle ADB.
In right triangle ADB, ∠ABD = 60°.
So, we can determine the trigonometric ratios of angle 60°.
Trigonometric Ratios of 0° and 90°
Consider the figure given below which shows a circle of radius 1 unit centered at the origin.
Let P be a point on the circle in the first quadrant with coordinates (x, y).
We drop a perpendicular PQ from P to the x-axis in order to form the right triangle OPQ.
Let ∠POQ = θ, then
sin θ = PQ / OP = y/1 = y (y coordinate of P)
cos θ = OQ / OP = x/1 = x (x coordinate of P)
tan θ = PQ / OQ = y/x
If OP coincides with OA, then angle θ = 0°.
Since, the coordinates of A are (1, 0), we have
If OP coincides with OB, then angle θ = 90°.
Since, the coordinates of B are (0, 1), we have
The six trigonometric ratios of angles 0°, 30°, 45°, 60° and 90° are provided in the following table.
You need to remember the above table by heart. Unfortunately there is no other option 🙁 . However you will solve really fun questions based on above ratios and also see their use in some interesting applications of trigonometry. You can now solve exercise 8.2 of NCERT.
If you need to resolve any doubt that might have arisen regarding the proof above, Click below👇 👇
Mnemonics for periodic table
Now it’s time for some fun Periodic table mnemonics (google if you don’t know meaning of this word :p), these will help you remember the S block and P block of the Periodic table. You also need to remember the corresponding element names apart from learning the above mnemonics, otherwise this would be a futile exercise. The entire objective is that you can write S block and P block elements on your own.
Group 1 is known as alkali metals. It includes Lithium (Li), Sodium (Na), Potassium (K), Rubidium (Ru), Caesium (Cs), and Francium (Fr).
Mnemonic for Group 1: H Li Na Kabra Se Frrar
Group 2 is known as alkaline earth metals. It includes Beryllium (Be), Magnesium (Mg), Calcium (Ca), Strontium (Sr), Barium (Br), and Radium (Ra).
Mnemonic for Group 2: Beta Mange Car Santro Baap Raazi
P-Block Elements: Consisting of last six groups of the periodic table (Groups 13 to 18), P-block elements have their valence electrons occupying p-orbitals.
Group 13 is known as Boron group or the group of Icosagens or Triels. It includes Boron (B), Aluminium (Al), Gallium (Ga), Indium (In), and Thallium (Tl).
Mnemonic for Group 13: Bring Aloo Gazar In Thali
Group 14 is known as Carbon group or the group of Crystallogens, Tetragens or Tetrels. It includes Carbon (C), Silicon (Si), Germanium (Ge), Tin (Sn), and Lead (Pb).
Mnemonic for 14: Chemistry Sir Get Some Problem
Group 15 is known as the group of Pnictogens or Nitrogen group. It includes Nitrogen (N), Phosphorus (P), Arsenic (As), Antimony (Sb), and Bismuth (Bi).
Mnemonic for Group 15: Nahi Pasand Aane Se Sab Bigade
Group 16 is known as the group of Chalcogens or Oxygen group. It includes Oxygen (O), Sulphur (S), Selenium (Se), Tellurium (Te), and the radioactive element Polonium (Po).
Mnemonic for Group 16: Oss Se Te Po
Group 17 is known as the group of Halogens. It includes Fluorine (F), Chlorine (Cl), Bromine (Br), Iodine (I), and Astatine (At).
Mnemonic for Group 17: Fir Cal Bahar Aayi Aunty
Group 18 is known as the group of Noble gases, excluding Helium. Normally, they are all odorless and colorless gases with very low chemical reactivity. The group includes Helium (He), Neon (Ne), Argon (Ar), Krypton (Kr), Xenon (Xe), and the radioactive Radon (Rn).
Mnemonic for Group 18: Heena Neena aur Kareena ke X-ray Rangeen.
To learn more about Periodic table mnemonics, click on the link below (watch only till 5:42).👇 👇
Attempt this quiz on Trigonometry and Periodic Table to test your knowledge👇 👇
Home made projector
The days are long, we crave to go to the movie theater but can’t because of the lock-down ,so what shall we do? Let’s bring theater home, not by buying it from the market but by creating it with our own hands.. Today, we will learn to make our own projector, so that we can watch movies in theater style. Let’s start.
Things that you will need – Shoe box, Cutter and scissors, Magnifying glass, Cello tape and your favorite movie.
Step 1: Making the Lens
Take your magnifying glass and take out the glass from it. (I had to unscrew mine from the base)
Center the glass on the front of the rectangular box that you have gathered.
Make an outline of the glass on the box.
- Using the box cutter, cut the outlined circle out. (You should have a circular hole on the front of your rectangular box)
5. Put your magnifying glass into the hole that you just made. To prevent it from falling, hold it in place with your hands for now.
Take your hot glue gun and apply the glue to where the glass and cardboard touch. (Be careful to not put glue on the lens! This can affect the projection quality)
Step 2: Making the Phone Holder
Take your ruler and measure the width of your rectangular box. (The width of mine is 6 3/8 inches) (Make sure to write this down on a piece of paper so that you may remember the measurements when making this with the cardboard)
This time, using the ruler, measure the height of a rectangular box. (The height of the box was 4 3/4 inches, but I chose to make the height of the phone holder 4 inches) (Make sure to write your measurement on a piece of paper so that you may remember the measurements when making this with the cardboard)
3. To make the back support for the phone holder, use your height and width to make a rectangle. (I decided to shorten (My rectangle was 4 inches by 6 3/8 inches)
4. To make the bottom support for the phone holder, use the measurement of the width, and for the height of the rectangle, divide the height of your back support rectangle by 2. This will be your height for the bottom support. (My rectangle was 2 inches by 6 3/8 inches)
5. Cut the rectangles out by following the outline of the rectangles that you have drawn.
6. Take your hot glue gun and attach the two rectangles, the longest sides touching each other.
7. Make sure the two rectangles together, form a right angle when looking at it from the side.
Step 4: How to Use the Projector
- Take your phone holder and lay it down on a flat surface
- Tape your phone down at the center of the holder. (Try to tape down the edges of the phone to the holder)
- Open the video, photo, or movie that you want to project.
- Hold the phone holder with the phone attached to it, upside down. (The photo, video, or movie should flip its view)
5. To lock your screen, (on an IOS device) swipe up from the bottom edge of the phone and click the Portrait Orientation Lock and if it is on, it should turn red-orange.
6. On that same screen, make sure your phone is at its highest setting.
7. Now, insert your phone holder into the projector body (making sure that the photo, video, or movie is still upside down)
8. Enter a dark room and play your photo, video, or movie
9. If the projection is blurry, focus it by moving the phone holder either backwards or forwards
Task
Since, you have watched your favourite movie. Now, it’s time to analyse the movie and learn something valuable from that( we should find something valuable from everything). So, critically analyze the movie and write about your favourite character and why is he or she your favourite . Do you like the character because you relate to them or you want to become like them ? What is the one quality you want to adopt from him or her . Give us a brief using the following link:
JIVAN GYAN
Today we will learn about 3 Mudra which practicing daily for 15min we can boost up OUR Memory and Concentration power. Click on learn more to watch the video explaining the same.
