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The variation of the values
As the Sine of an angle increases the Cosine of the angle decreases from the value 0 to 1 and vice vers..
Summary
Trigonometric tables are used - to find the value of a t-ratio when the angle is given - to find the angle when the value of the t-ratio is given As an angle increases, the sine ratio increases, the cosine ratio decreases and the tangent ratio increases...
Graph of y = sin x
As x increases from 180 o to 270 o , sinx decreases from 0 to -1 and as x increases from 270 o to 360 o , sinx increases from -1 to 0. The maximum absolute value of sin x = ..
Graph:
From the graph it is clear that the curve repeats itself every 360 o (2 p rad). This fact is expressed by the statement that the function has a period of 360 o (2 p radians). In symbols we write cos(x + 360 o .n) = cos(x + 2 p n) = cos x where n is a positive or negative integer. From the gra..
From the graph it is clear that the curve repeats itself every 360 o (2 p rad). This fact is expressed by the statement that the function has a period of 360 o (2 p radians). In symbols we write cos(x + 360 o .n) = cos(x + 2 p n) = cos x where n is a positive or negative integer. From the gra..T-ratios of 0o and 90o
We observe A"B" > A'B' > AB, denominator remains 'r' (radius). As the angle increases sine ratio increases. We observe OB'' < OB' < OB, denominator remains r. As the angle increases cosine ratio decreases, When a = ..
We observe A"B" > A'B' > AB, denominator remains 'r' (radius). As the angle increases sine ratio increases. We observe OB'' < OB' < OB, denominator remains r. As the angle increases cosine ratio decreases, When a = ..Solved Examples
1. At a point 50 m from the foot of a building, the angle of elevation of the top of the building is 70 o 36 ' . Find the height of the building. 2. The shadow of a vertical lower on level ground increased by 10 m when the altitude of the sun changed from 45 o to 30 o . Usin..
Natural Tangent Tables
>The integral 1 is not repeated in every column. So look in column 0 ' for the integral part or in the preceding horizontal column in B group as the case may be. (ii) tan 51 o 18 ' Look horizontally along 51 o column and vertically under 18 ' in B group. tan 51 o 18 ' = 1.248 (iii) tan 51 o 23 ' As..
Natural Sine Tables
sin 56 o 24 ' = 0.8329 (iii) sin 56 o 28 ' As in (ii) read for sin 56 o 24 ' and for 4 ' read from 'C' group. sin 56 o 24 ' = 0.8329 mean difference for 4 ' = 7 to be added sin 56 o 28 ' = 0.8336 As the angle has increased, sine ratio has increased. To find q when sine ratio is ..
sin 56 o 24 ' = 0.8329 (iii) sin 56 o 28 ' As in (ii) read for sin 56 o 24 ' and for 4 ' read from 'C' group. sin 56 o 24 ' = 0.8329 mean difference for 4 ' = 7 to be added sin 56 o 28 ' = 0.8336 As the angle has increased, sine ratio has increased. To find q when sine ratio is ..Solved Examples
BC = 50 x tan 70 o 36 ' = 50 x 2.840 = 142.0 m BC = 142.0 m The shadow of a vertical lower on level ground increased by 10 m when the altitude of the sun changed from 45 o to 30 o . Using the given figure, find the height of the tower, correct to one place of decima..
Increasing and Decreasing Functions
Increasing and Decreasing Functions - This section explains how derivative can be used to check whether a function is increasing, decreasing or neither increasing nor decreasing in its domain. Let f be a function defined on an interval I a..
Increasing and Decreasing Functions - This section explains how derivative can be used to check whether a function is increasing, decreasing or neither increasing nor decreasing in its domain. Let f be a function defined on an interval I a.. Result
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