Facts that Matter
• Tangent to a Circle
A tangent to a circle is a line that touches the circle at only one point.
Theorem 1
The tangent at any point of a circle is perpendicular to the radius, through the point of contact.
Proof: We have the centre O of the given circle and XY is the tangent to the circle at a point P.
Let us take a point Q on Xy other than P, Join OQ.
Obviously, Q lies outside the circle.
i.e., OQ > OP
Since, all the points on XY, except P lies outside the circle.
i.e., OP is smaller than all the distance of the point O from XY.
i.e., OP is the smallest distance of O from XY.
i.e., OP ⊥ XY
Area related to circle
Coordinate Geometry-Notes
Trigonometric ratios
• The certain ratios involving the sides of a right angled triangle are called Trigonometric ratios.
Suppose: b is the base
h is the hypotenuse
p is perpendicular
then,
Reciprocals of the ratios are:
Cosec A= 1/sin A= h/p
Sec A= 1/cos A= h/b
Cot A= 1/tan A= b/p
• Sin □ is a single symbol and sin cannot be detached from ‘□’. And sin □ ≠ sin X □.
This remark is true for other ratios as well
Trigonometric /Ratios of some specific angles
The specific angles are 0°, 30°,45°, 60°, 90°. These are given in the following table
The value of sin A increases from 0 to 1, as A increases from 0° to 90°
The value of cosA decreases from 1 to 0, as A increases from 0° to 90°
The value of tan A increases from 0 to infinity, as A increases 0° to 90°
√2 = 1.414 and √3 = 1.732
Trignometric identitiex
• Cos2 A+ sin2 A = 1
• 1+tan2 A= sec2 A
• Cot2 A+1= cosec2 A
Trigonometric ratios of complementary angles
Two angles are said to be complementary if their sum equals to 90°
1. Sin (90°-A)= cos A
2. Cos (90°-A)= sin A
3. Tan (90°-A)= cotA
4. Cot (90°-A)= tan A
5. Sec (90°- A)= cosec A
6. Cosec( 90°- A)= sec A
Note
Tan 0°= cot 90°= 0
Sec0°=cosec 90°=1
Sec 90°, cosec 0°, cot 0° and tan 90° are not defined
Volume surface area
No comments:
Post a Comment