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vagabundo [1.1K]
3 years ago
8

Sketch a unit circle and label the terminal points corresponding to theta=pi/4, 3pi/4, 5pi/4, 7pi/4 Include the coordinates of e

ach point
Mathematics
1 answer:
slavikrds [6]3 years ago
3 0

Answer:

Did you ever figure out the answer to this question? And if so, did you figure out how to solve it.

Step-by-step explanation:


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Cot y, if csc y =-10/3 and cos y< 0
fredd [130]
\csc y=-\dfrac{10}3\implies\sin y=-\dfrac3{10}

\cos^2y=1-\sin^2y\implies \cos y=\pm\sqrt{1-\dfrac9{100}}=\pm\dfrac{\sqrt{91}}{10}

You're told that \cos y, so omit the positive root.

\cot y=\dfrac{\cos y}{\sin y}=\dfrac{-\frac{\sqrt{91}}{10}}{-\frac3{10}}=\dfrac{\sqrt{91}}3
7 0
3 years ago
The vertices of a parallelogram are A(x1, y1), B(x2, y2), C(x3, y3), and D(x4, y4). Which of the following must be true if paral
Iteru [2.4K]

The answer is really none of the above, because all of these have divisions by difference in x, and there are perfectly fine rectangles where those will mean dividing by zero.

To do the problem the way they want us to, we note segments with the same slope are parallel (or collinear); segments with slopes which multiply to -1 are perpendicular.

Let's figure out what each choice is trying to tell us by translating it into parallel and perpendicular. Remember A is point 1, ...

A. ((y_4-y_3)/(x_4-x_3)= (y_3-y_2)/(x_3-x_2)) and ((y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2))=-1

translated, that's CD║BC and CD⊥BC - contradictory; second half right

B. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and ((y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1))=-1

CD ║ AB and CD ⊥ AB - only the parallelogram half is right

C. (y_4-y_3)/(x_4-x_3)= (y_2-y_1)/(x_2-x_1) and (y_4-y_3)/(x_4-x_3)×(y_3-y_2)/(x_3-x_2)=-1

CD║AB and CD⊥BC - that's TRUE

D. (y_4-y_3)/(x_4-x_3)= (y_3-y_1)/(x_3-x_1) and (y_4-y_3)/(x_4-x_3)×(y_2-y_1)/(x_2-x_1)=-1

CD║AC and CD⊥AB - nope

Answer: C

The way I'd get the proper expression is with the dot product.

A parallelogram is a rectangle when adjacent sides are perpendicular. It only takes one right angle to make them all right.

Two sides are perpendicular when the dot product of their direction vectors is zero. All the answers have y_4 - y_3 so one side is CD. The other side must be BC or AD; AD would give y_4 - y_1 terms which don't appear among the answer, so let's go with BC.

The direction vectors are

D-C = (x_4 - x_3, y_4 - y_3)

C-B = (x_3 - x_2, y_3 - y_2)

For perpendicularity we need a zero dot product:

0 = (D-C)\cdot(C-B) = (x_4 - x_3)(x_3 - x_2) + (y_4 - y_3)(y_3 - y_2)

- (x_4 - x_3)(x_3 - x_2) = (y_4 - y_3)(y_3 - y_2)

That's the correct expression, given it's a parallelogram, to demonstrate it's a rectangle. The divisions make it iffy.

8 0
2 years ago
For the given angle 0, identify the reference angle, _
ankoles [38]

Answer:

π\6

Step-by-step explanation:

The reference angle is the smallest angle measured from the terminal side of the angle (where the angle ends) to the x axis. The reference angle is an acute angle (i.e less than 90° or π/2)

For O = 11π/6 = 1.833π

1.833π is in the fourth quadrant between 3π/2 radians and 2π radians. Since it is in the fourth quadrant, the reference angle is given as:

reference angle = 2π - 11π/6 = π\6

5 0
3 years ago
What is 4.7 x 4.75 =
UNO [17]
The answer for this is 22.325
6 0
3 years ago
What vertex does the quadrilateral and the pentagon share?
Leokris [45]
It equals the middle
7 0
3 years ago
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