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3 years ago

Find the rectangular coordinates of the point (square root of 3, pi/6)

Mathematics

1 answer:

natima [27]3 years ago

5 0

Answer:

x = 1.5

y = 0.866

Step-by-step explanation:

To convert from polar coordinates to rectangular coordinates, we can use the following formulas:

x = r * cos(theta)

y = r * sin(theta)

So, if our point if (sqrt(3), pi/6), that means r = sqrt(3) and theta = pi/6, so we have that:

x = sqrt(3) * cos(pi/6) = sqrt(3) * sqrt(3)/2 = 3/2 = 1.5

y = sqrt(3) * sin(pi/6) = sqrt(3) * 1/2 = sqrt(3)/2 = 0.866

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Step-by-step explanation:

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3 years ago

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rosijanka [135]

Answer:

Step-by-step explanation:

To solve this equation, we need the formula for perfect squares:

$(a + b)^2 = a^2 + 2ab + b^2$

$(a - b)^2 = a^2 - 2ab + b^2$ <em>this is the formula we will use because the signs match the one in the question</em>.

Knowing these, we can set up an equation that assumes that the answer we will end up with is a perfect square.

Work:

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this is the setup for being able to solve for the unknown $x$ , now we need to solve for $x$ .

$(v - x)^2 = v^2 - 8v + x^2$ (I replaced $2ab$ with $8v$ because I'm setting up this question to be a perfect square).

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Divide like terms and isolate the variable. In this case, $v^2$ and $x^2$ are on both sides, so dive them and they will be canceled out.

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divide by $2v$ and you will have your value for $x$ .

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4 years ago

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dexar [7]

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3 years ago

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Goryan [66]

Answer:

x=23°; θ=87°

Step-by-step explanation:

These two angles create what is known as supplementary angles, or 2 angles that add up to 180°. We know this because all horizontal lines are 180° on either side. Since we know the total value of these two angles should equate to 180°, we can set up a simple equation:

$93+(3x+18)=180$

Now, using algebra, we can solve for x:

$111+3x=180$

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$x=23$

Plugging x back into the equation, we get:

$3(23)+18=87$

Therefore, the total angle is equal to 87° and x is equal to 23°.

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