Answer
Coordinates of point B- (4,3)
Asked T-functions-
$\sin A = \frac{3}{5}$
$\cos A = \frac{4}{5}$
$\tan A = \frac{3}{4}$
Work Step by Step
Steps to solution-
Given that angle A is in standard position-
Length AC = 4
Therefore x-coordinate of point B is '4' as it is the distance traveled along positive direction of x-axis.
Length BC = 3
Therefore y-coordinate of point B is '3' as it is the distance traveled along positive direction of y-axis.
Hence (4,3) are the coordinates of point B.
Solution for T-functions-
Considering triangle ABC right angled at C
BC = 3 = a
AC = 4 = b (concluded from above solution)
Using this data and Pythagoras Theorem to solve for 'c'-
$c^{2} =a^{2} + b^{2}$ ( Pythagoras Theorem)
$c^{2} = 3^{2} + 4^{2}$
$c^{2} = 9 + 16$
$c^{2} = 25$
c = 5
Now we can write the asked T-functions of A using a = 3, b=4 and c = 5
$\sin A = \frac{a}{c} = \frac{3}{5}$
$\\cos A = \frac{b}{c} = \frac{4}{5}$
$\\tan A = \frac{a}{b} = \frac{3}{4}$
