TRIGNOMETRY_Lectures_Discussion_Cla.pptx

It contains details of Trigonometry

1. TRIGONOMETRY FOR CLASS 10 BY-SUDHANSHU SABHARWAL B.TECH(CIVIL ENGINEERING) 2015

2. TRIGONOMETRY Trigonometry is derived from Greek words trigonon (three angles) and metron (measure ). Trigonometry is the branch of mathematics which deals with triangles, particularly triangles in a plane where one angle of the triangle is 90 Degree. Trigonometry specifically deals with relationships between the sides and the angles of a triangle, i.e. on the trigonometric functions, and with calculations based on these functions.

3. Right Triangle A triangle in which one angle is equal to 90 degree is called a right angled triangle . The side opposite to the right angle is known as hypotenuse . AC is the hypotenuse The other two sides are known as legs or base and altitude AB and AC are base and altitude respectively

4. RIGHT ANGLE

5. Pythagoras Theorem In any right triangle, the area of the square whose side is the hypotenuse is equal to the sum of the areas of the squares whose sides are the two legs . In the figure , AC 2 = AB 2 + BC 2

6. Pythagoras theorem example AC 2 +BC 2 =AB 2 AC=4,BC=3

7. WHY TRIGONOMETRY See in Pythagoras theorem we have given two sides and using theorem formula we can find the third side But in few questions we know the dimension of one side only and we find other two sides using trigonometry

8. SURVEYING

9. Value for Trigonometric Functions for Angle C   Sinθ = AB/AC Cos θ = BC/AC Tanθ = AB/BC Cosecθ = AC/AB Secθ = AC/BC Cotθ = AC/AB

10. APPLICATIONS Measuring inaccessible lengths Height of a building (tree, tower, etc .) Width of a river (canyon, etc.)

11. HOW TO MAKE A TABLE OF TRIGONOMETRIC FUNCTIONS FIRSTLY WRITE DOWN THE FUCTIONS ON LEFT SIDE - SIN,COT,TAN,COSEC,SEC,COT THEN WRITE DOWN THE ANGLES ON THE TOP 0,30,45,60,90 DEGREE THEN WRITE STARTING FROM THE ZERO DEGREE TO 90 – 0,1,2,3,4 AND DIVIDE THEM BY 4 AND TAKE SQUARE ROOT OF THEM

12. CONTINUE THE VALUES WE OBTAINTED FROM THIS ARE THE VALUES OF SIN THEN FOR COS WRITE DOWN THE VALUES OF SIN FROM ORDER 90,60,45,30,0 LIKE SIN 90= COS 0, SIN 60=COS 30, SIN 45= COS 45, SIN 30= COS 60,SIN 0= COS 90 NOW TAN= SIN/COS SO WE DIVIDE THE VALUES OF ANGLES FOR THE TAN

13. CONTINUE WHEN 0 COMES IN THE DENOMINATOR THE FRACTION BECOMES INFINTY ∞ FOR COSEC= 1/ SIN SO WE REVERSE THE VALUES OF SIN FOR THIS FOR SEC=1/COS SO WE REVERSE THE VALUES OF COS FOR THIS FOR COT=1/TAN SO WE REVERSE THE VALUES OF TAN FOR THIS