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attashe74 [19]
2 years ago
5

Q, S, T, and U are coplanar: true or false? Why?

Mathematics
1 answer:
inysia [295]2 years ago
7 0
I think it would be true because they are crossing
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Which of the following is not equal to sin⁡(-230°)?
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From trigonometry we know that:

if sin(\theta)=sin(\alpha)

then, \theta=n\pi+(-1)^n\alpha (where n is an integer)

This can be rewritten in degrees as:

\theta=n(180^{\circ})+(-1)^n\alpha.............(Equation 1)

Now, in our case, \alpha=-230^{\circ}

Therefore, (Equation 1) can be written as:

\theta=n(180^{\circ})+(-1)^n(-230^{\circ})..........(Equation 2)

Now, to find the correct options all that we have to do is replace n by relevant integers and find the values of \theta that match.

For n=2, (Equation 2) gives us: \theta=2\times 180^{\circ}+(-1)^2(-230^{\circ})=360^{\circ}-230^{\circ}=130^{\circ}.

Thus, sin(230^{\circ})=sin(130^{\circ})

Now, we know that: -sin(-50^{\circ})=sin(50^{\circ})

Let n=-1, then:

\theta=(-1)\times 180^{\circ}+(-1)^{-1}(-230^{\circ})=-180^{\circ}+230^{\circ}=50^{\circ}

Thus, sin(-230^{\circ})=-sin(-50^{\circ})

Likewise, sin(-230^{\circ})=sin(50^{\circ})

Only the last option sin(-50^{\circ}) will never match sin(-230^{\circ}) because no integral value of n will ever give \theta=-50^{\circ}

Thus the last option is the correct option.

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A square is inscribed in a circle . If the area of the square is 9 inch square what is the ratio of the radius of the circle to
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Answer:

  (√2)/2

Step-by-step explanation:

The ratio of the radius of the circle to the side of the inscribed square is the same regardless of the size of the objects.

The radius of the circle is half the length of the diagonal of the square. For simplicity, we can call the side of the square 1, so its diagonal is √(1²+1²) = √2 by the Pythagorean theorem. The radius is half that value, so is (√2)/2. The desired ratio is this value divided by 1.

Scaling up our unit square to one with a side length of 3 inches, we have ...

  radius/side = ((3√2)/2) / 3 = (√2)/2

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A square with a side length of 3 inches will have an area of (3 in)² = 9 in².

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An angle that is less than 180 degrees is acute. Always Sometimes Never
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Answer:

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Step-by-step explanation:

An acute angle is an angle that measures less than 90°

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