Saturday, December 28, 2013

77-Basics of Trigonometry - 05 Important key points

Today we will study trigonometric ratios of 90°, 180°, and 270°.

5) Trigonometric ratios of an angle O = 90°
Here angle AOP is of 90°.
According to the diagram, OP = r and the coordinates of point P are (0, r). So x-coordinate of point P is 0 and the y-coordinate of point P is r.
So, all the trigonometric ratios of O = 90° with
 x = 0, y = r, r = r.
a) sin 90° = y/r
    sin 90°  = r/r   
    sin 90°  = 1
b) cos 90° = x/r
     cos 90° = 0/r
     cos 90° = 0
c) tan 90° = y/x
    tan 90°  = r/0  
    tan 90°  = ∞
d) csc 90° = r/y
    csc 90° =  r/r
    csc 90° =  1
e) sec 90° = r/x
    sec 90° = r/0          sec 90° = ∞
f) cot 90° = x/y
    cot 90° = 0/r   
    cot 90° = 0


Friday, December 27, 2013

76-Basics of Trigonometry - 04 Important key points

Now we will study the next part of trigonometry. 

Today we will study trigonometric ratios of 0°, 30°, 45°, 60°.

1) Trigonometric ratios of an angle =  0°

Here angle AOP is of 0°.
According to the diagram, OP = r and the coordinates of point P are (r, 0). So x-coordinate of point P is r and the y-coordinate of point P is 0.

So, all the trigonometric ratios of 0° with
 x = r,
 y = 0,
 r  = r.

Tuesday, December 24, 2013

75-Basics of Trigonometry - 03 Important key points

Now we will study the next part of trigonometry. 

Today we will study Angles in standard position, positive and negative angles, the definition of trigonometric ratios in the Cartesian coordinate system and Signs of trigonometric ratios in different quadrants.

Angles in standard position:

1) Ray OA is an Initial Ray.
2) Rotate ray OA in Anti-Clock-Wise direction through certain angle keeping point O as a fixed point.
3) The final position of ray OA is the ray OB which is known as a Terminal ray.
4) Here an angle AOB made by these two rays (Ray OA & Ray OB) with fixpoint O as the vertex is known as the directed angle.