answer to question number 108 page 40 for algebra and trigonometry

C = 180 o - (25 + 108 o ) = 47 o Taking log on both sides, we get log b = log a + log (sin B) - log (sin A) = log 18 + log (sin 180 o ) - log (25 o ) = log 18 + log (sin 72 o ) - log (25 o ) = log 18 + log (0.9511) - log (0.4226) (from Trigonometric table) = 1.2553 - 1 + 0.9782 + 1..

The number of radians in angle subtend by an arc of a circle at the Let . Now draw a circle of radius r which intersect OP at A and OQ at C. Consider an arc AB on the circle, so that the length of the arc and the length of radius are both equal to r. Draw OB. Then by definition of..

Some Trigonometrical Identities - 1. sin A = cos (90 o - A) 2. 3. tan A x tan (90 o - A) = 1 4. sin 2 A + cos 2 A = 1 5. 1 + tan 2 A = sec 2 A 6. 1 + cot 2 A = cosec 2 A Let us prove the above identities. Let D ABC be a right-angled triangle with B = 90 o . Let BC = a, AC = b and AB = c. (..

x + y = 7 (1) When the digits are reversed, the new number becomes = 10y + x New number increased by 3 = 4 times the original number (10y + x) + 3 = 4 (10x + y) or 10y + x + 3 = 40x + 4y 10y + x - 40x - 4y = -3 -39x + 6y = -3 - 13x + 2y = -1 (Dividin..

Let x be the required number. The value of x is determined by solving the equation. Thus \ 2x + x = 36 \ 3x = 36 \ x = 12 \ The number is 12. A man walking at the rate of four kilometres an hour, covers a certain distance in three hours less than another who walks at the rate of..

An irrational root of a positive rational number is called a surd. Consider a number with base 'a' as a positive rational number with power of a fraction, say then Since is an n t h root, it is called a surd of order n, if it is irrational. e.g., (i)..

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 combinations. Each ratio i..

Graphs - In algebra we found that the graph of algebraic functions helped greatly in studying the properties of the function. For the same reason, we shall study the graph of trigonometric functions. In plotting the graph of any trigonometric function the angle may be regarded a..

Solve the triangle ABC, given a =18, A = 25 o , B = 108 o..

In plotting the graph of any trigonometric function the angle may be regarded as measured either in radians or in degrees. If a trigonometric function is combined with an algebraic function it is customary to assume that the angle is measure in radian..