We have been given that point a is at and point c is at
. We are asked to find the coordinates of point b on segment ac such that the ratio is 1:3.
We will use section formula to solve our given problem.
When point P divides a segment internally in the ratio m:n, the coordinates of point P would be:
Let point and point
.
Therefore, the coordinates of point 'b' would be .
Answer:
i) sin(2x) =
ii) cot(x+360) =
iii) sin(x-180) =
Step-by-step explanation:
sec(x) = 2
Since cos(x) is reciprocal of sec(x), this means:
cos(x) =
cosec(x) is negative , this means sin(x) is also negative. The only quadrant where cos(x), sec(x) are positive and sin(x), cosec(x) are negative is the 4th quadrant. Hence the terminal arm of the angle x is in 4th quadrant.
Part i)
sin(2x) can be simplified as:
sin(2x) = 2 sin(x) cos(x)
First we need to find the value of sin(x). According to Pythagorean identity:
Since, angle is in 4th quadrant, sin(x) will be negative. So considering the negative value of sin(x) and substituting the value of cos(x), we get:
So,
Part ii)
We have to find cot(x + 360)
An addition of 360 degrees to the angle brings it back to the same terminal point. So the trigonometric ratios of the original angle and new angle after adding 360 or any multiple of 360 stay the same. i.e.
cot(x + 360) = cot(x)
Using the values, we get:
Part iii)
We need to find the value of sin(x - 180)
sin(x - 180) = - sin(x)
Addition or subtraction of 180 degrees changes the angle by 2 quadrants. The sign of sin(x) becomes opposite if the angle jumps by 2 quadrants. For example, sin(x) is positive in 1st quadrant and negative in 3rd quadrant.
So,
sin(x - 180) =