The augmented matrix is given for a system of equations. If the system is consistent, find the general solution. Otherwisestate
that there is no solution. Use x1, x2, x3 as variables.
1 answer:
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Ans: Option (1) <span>Discontinuity at (1, 7), zero at ( negative four thirds , 0)
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Explanation:
Given function:
Now if we plug in the x = 1, we would have discontinuity as function goes to infinity.
Now for f(1):
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Explanation:
Given function:
Now if we plug in the x = 1, we would have discontinuity as function goes to infinity.
Now for f(1):
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) =