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vodka [1.7K]
3 years ago
7

Find the tangent of angle Z.

Mathematics
1 answer:
Elza [17]3 years ago
3 0

\tan Z = \dfrac{ \textrm{opp}}{\textrm{adj}} = \dfrac{8}{6} = \dfrac{4}{3}

Tangent Z: 4/3

\cos Y = \dfrac{\textrm{adj}}{\textrm{hyp}} = \dfrac{8}{10} = \dfrac 4 5

Cosine Y: 4/5

\cot Y= \tan Z = \dfrac 4 3

Cotangent Y: 4/3

\sin Y = \dfrac{ \textrm{opp}}{\textrm{hyp}} = \dfrac{6}{10} = \dfrac{3}{5}

\sec Z = \dfrac{1}{\cos Z} = \dfrac{1}{\sin Y} = \dfrac{5}{3}

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exis [7]
Take the derivative with respect to t
- w \sin(wt) + \sqrt{8} w cos(wt)
the maximum and minimum values occur when the tangent line is zero so we set the derivative to zero
0 = -w \sin(wt) + \sqrt{8} w cos(wt)
divide by w
0 =- \sin(wt) + \sqrt{8} cos(wt)
we add sin(wt) to both sides

\sin(wt)= \sqrt{8} cos(wt)
divide both sides by cos(wt)
\frac{sin(wt)}{cos(wt)}= \sqrt{8}   \\  \\ arctan(tan(wt))=arctan( \sqrt{8} ) \\  \\ wt=arctan(2 \sqrt{2)} OR\\ wt=arctan( { \frac{1}{ \sqrt{2} } )
(wt)=2(n*pi-arctan(2^0.5))
(wt)=2(n*pi+arctan(2^-0.5))
where n is an integer
the absolute max and min will be

I=cos(2n \pi -2arctan( \sqrt{2} ))
since 2npi is just the period of cos
cos(2arctan( \sqrt{2} ))= \frac{-1}{3} 

substituting our second soultion we get
I=cos(2n \pi +2arctan( \frac{1}{ \sqrt{2} } ))
since 2npi is the period
I=cos(2arctan( \frac{1}{ \sqrt{2}} ))= \frac{1}{3}
so the maximum value =\frac{1}{3}
minimum value =- \frac{1}{3}


4 0
3 years ago
Which coordinate plane shows the graph of the function y = ?
Brilliant_brown [7]
Y=1/2 x so graph B i think.
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3 years ago
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The width of rectangle A is the sum of twice a number and 8. The length of the rectangle is 3 times as great as the width. If th
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Formula for perimeter of a rectangle = 2(L + W)
let the number be x
width = 2x + 8
length = 3(2x + 8)
substitute respectively
96 = 2 (2x + 8 + 3(2x + 8)) open the bracket
96 = 2 ( 2x + 8 + 6x + 24) collect like terms
96 = 2 (8x + 32) open the bracket
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collect like terms
96 - 64 = 16x
32 = 16x
divide both sides by 16
32/16 = 16x/16
2 = x
therefore, the width = 2x + 8 = 2(2) + 8 = 4 + 8 = 12.
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4 0
3 years ago
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Harlamova29_29 [7]

<em>Answer:</em>

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<em>Step-by-step explanation:</em>

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<em>and so on. </em>

<em>Hope this helps. Have a nice day.</em>

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Answer:

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