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4 years ago

What is the measure of the angle in standard position?

Mathematics

1 answer:

mars1129 [50]4 years ago

3 0

Answer:

Step-by-step explanation:

What's inside the set of parenthesis is a description of the angle in terms of cos and sin. This says that the angle has a cos of square root of 3 over 2, and a sin of negative 1 over 2.

The cos of this angle is the line directly horizontal ON the x axis, since cos is the same as x.

The sin of this angle is the line that would be there if you dropped an altitude from the arrow on the x line to the arrow on the other line.

The tangent ratio, being side opposite over side adjacent will give us the angle we need. Use the inverse tangent and enter in those values and you'll get that the angle is -30.

even easier than that, look at your unit circle to see where there is a cos, sin combination of those values. It will be located at -30 degrees, which is also 330 degrees.

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vredina [299]

Answer:

a. $M(x,y) = (-1,-1)$

b. $D(-4,-9)$

Step-by-step explanation:

Given

A(-8,7) and B(6,-9).

Solving (a):

Determine the Midpoint M;

This is calculated as follows;

$M(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Where

$(x_1,y_1) = (-8,7)$

$(x_2,y_2) = (6,-9)$

Substitute these values in the formula

$M(x,y) = (\frac{-8+6}{2},\frac{7-9}{2})$

$M(x,y) = (\frac{-2}{2},\frac{-2}{2})$

$M(x,y) = (-1,-1)$

<em>Hence; the midpoint is (-1,-1)</em>

Solving (a):

Here, we have

C = (2,7)

M; Midpoint = (-1,-1)

Required: Determine D

This is calculated as follows;

$M(x,y) = (\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})$

Where

$(x_1,y_1) = (2,7)$

$(x,y) = (-1,-1)$

Substitute these values in the formula

$(-1,-1) = (\frac{2+x_2}{2},\frac{7+y_2}{2})$

Solving for x2

$-1 = \frac{2 + x_2}{2}$

Multiply both sides by 2

$-2 = 2 + x_2$

Subtract 2 from both sides

$x_2 = -2 - 2$

$x_2 = -4$

Solving for y2

$-1 = \frac{7 + y_2}{2}$

Multiply both sides by 2

$-2 = 7 + y_2$

Subtract 7 from both sides

$y_2 = -2 - 7$

$y_2 = -9$

Hence, the coordinates of D is

$D(-4,-9)$

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4 years ago

Which equation represents the line that passes through points (0, 6) and (2, 0)? A.)y = negative one-third x + 2 B.)y = negative

Rudiy27

Find the slope of the line through (x1,y1) = (0,6) and (x2,y2) = (2,0)

m = (y2 - y1)/(x2 - x1)

m = (0 - 6)/(2 - 0)

m = -6/2

m = -3

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Since we're given the point (0,6) to be on the line, we know the y intercept is b = 6.

Plug m = -3 and b = 6 into y = mx+b to get y = -3x+6

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3 years ago

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3 years ago

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Answer:

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