Trigonometry
Trigonometry - With trigonometry we can find the height of a building or the width of a river without actually climbing or crossing. Certain basic definitions are necessary to further develop this subject. The ratios of two sides of a triangle are taken. There are six possible c..
Trigonometry - With trigonometry we can find the height of a building or the width of a river without actually climbing or crossing. Certain basic definitions are necessary to further develop this subject. The ratios of two sides of a triangle are taken. There are six possible c..Statement:
(i) 1 + tan 2 x = sec 2 x (ii) 1 + cot 2 x = cosec ..
Note:
i) The numerical values of sin q and cos q cannot be greater than 1. ii) The numerical values of sec q and cosec q can never be less than 1. iii) There is no restriction on the values of tan q and cot q since they can take any valu..
i) The numerical values of sin q and cos q cannot be greater than 1. ii) The numerical values of sec q and cosec q can never be less than 1. iii) There is no restriction on the values of tan q and cot q since they can take any valu..Method II
a cos q + b sin q = c -----(i) (i) can be written as or a (1- t 2 ) + 2bt - c (1+t 2 ) = 0 This is a quadratic in 't' and can be solved...
a cos q + b sin q = c -----(i) (i) can be written as or a (1- t 2 ) + 2bt - c (1+t 2 ) = 0 This is a quadratic in 't' and can be solved...Note:
i) Angle 0 o : If there is no rotation, ie., the initial side and the terminating side of the angle coincides then the angle measure is 0 o . ii) If a radius vector makes a ' n' number of rotations and finally stops at a position then the angle is [(360)(n) + q ] o The measure of t..
i) Angle 0 o : If there is no rotation, ie., the initial side and the terminating side of the angle coincides then the angle measure is 0 o . ii) If a radius vector makes a ' n' number of rotations and finally stops at a position then the angle is [(360)(n) + q ] o The measure of t..Proof:
(i) sin[(x+y) + z] (ii) cos[(x+y) + z] ..
(i) sin[(x+y) + z] (ii) cos[(x+y) + z] ..Particular Cases
i) If sin q = 0, then a = 0. Hence, we get q = n p + (-1) n 0 = n p . ..
i) If sin q = 0, then a = 0. Hence, we get q = n p + (-1) n 0 = n p . ..1st Method:
>This problem is made up of two separate simple problems. AC is the tower. (i) To find BC, distance of the boat from the tower. AC is tower. is the angle of depression. B = 29 o (alternate ) = 61 o (why do we find it?) BC = 180 x tan 61 o . = 180 x 1.804 = 324.72 = 325 m. (ii) To fi..
>This problem is made up of two separate simple problems. AC is the tower. (i) To find BC, distance of the boat from the tower. AC is tower. is the angle of depression. B = 29 o (alternate ) = 61 o (why do we find it?) BC = 180 x tan 61 o . = 180 x 1.804 = 324.72 = 325 m. (ii) To fi..T-ratios of 0o and 90o
When (infinity) As the angle increases tangent ratio increases. From the above results we conclude that for an acute angle q , the following results hold good. (i) (i..
When (infinity) As the angle increases tangent ratio increases. From the above results we conclude that for an acute angle q , the following results hold good. (i) (i..See what our Users say :
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