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Gnesinka [82]
3 years ago
11

Cos(2x) + sin^2(x) = 0

Mathematics
1 answer:
zloy xaker [14]3 years ago
7 0

cos(2<em>θ</em>) + sin²(<em>θ</em>) = 0

Half-angle identity:

cos(2<em>θ</em>) + (1 - cos(2<em>θ</em>))/2 = 0

Simplify:

2 cos(2<em>θ</em>) + 1 - cos(2<em>θ</em>) = 0

cos(2<em>θ</em>) = -1

Solve for <em>θ</em> :

2<em>θ</em> = arccos(-1) + 2<em>nπ</em>

2<em>θ</em> = <em>π</em> + 2<em>nπ</em>

<em>θ</em> = <em>π</em>/2 + <em>nπ</em>

where <em>n</em> is any integer.

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Fiesta28 [93]

Answer:

1) 1.1 seconds

2) 13.5 feet

<h3>Part A</h3>

\rightarrow \sf  -16t^2 + 5t + 15 = 0

<u>Apply quadratic formula</u>:

\rightarrow \sf t=   \dfrac{-5\pm \sqrt{5^2-4\left(-16\right)\cdot \:15}}{2\left(-16\right)}

<u>Simplify following</u>

\rightarrow \sf t=-\dfrac{-5+\sqrt{985}}{32},\:t=\dfrac{5+\sqrt{985}}{32}

In decimal form:

\rightarrow \sf t=-0.825 ,\:t=1.137

Conclusion:

As time is be only positive: t = 1.1 seconds

<h3>Part B</h3>

\rightarrow \sf  h=-16t^2 + 5t + 15

<u>insert t = 0.5</u>

\rightarrow \sf  h=-16(0.5)^2 + 5(0.5) + 15

<u>simplify</u>

\rightarrow \sf  h=13.5

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2 years ago
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The one is the same everywhere so we ignore it.


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