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Answer:
Step-by-step explanation:
Saving the long, drawn out derivation of the formulas to find the x and y coordinates of the directed point, suffice it to say that it is:
x coordinate: and
y coordinate:
where x1, x2, y1, and y2 are the coordinates from the given points and a and b are the numbers in the ratio, namely a = 3 and b = 4. Filling in accordingly:
the x coordinate of the directed point is
which simplifies down to -6, and
the y coordinate of the directed point is
which simplifies down to -1.
The coordinate of the point is (-6, -1). Write that down so you don't forget it.
First lets see the pythagorean identities
So if we have to solve for sin theta , first we move cos theta to left side and then take square root to both sides, that is
Now we need to check the sign of sin theta
First we have to remember the sign of sin, cos , tan in the quadrants. In first quadrant , all are positive. In second quadrant, only sin and cosine are positive. In third quadrant , only tan and cot are positive and in the last quadrant , only cos and sec are positive.
So if theta is in second quadrant, then we have to positive sign but if theta is in third or fourth quadrant, then we have to use negative sign .