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baherus [9]
3 years ago
6

{2n}^{2} + 3" alt="g(n) = - {2n}^{2} + 3" align="absmiddle" class="latex-formula">
Find g(6)
Mathematics
1 answer:
RideAnS [48]3 years ago
6 0

\bf g(n)=-2n^2+3\qquad \qquad g(\stackrel{\stackrel{n}{\downarrow }}{6})=-2(6)^2+3\implies g(6)=-2(36)+3 \\\\\\ g(6)=-72+3\implies g(6)=-69

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Find , , and if and terminates in quadrant .
ioda

sin2x =12/13

cos2x = 5/13

tan2x = 12/5

STEP - BY - STEP EXPLANATION

What to find?

• sin2x

,

• cos2x

,

• tan2x

Given:

tanx = 2/3 = opposite / adjacent

We need to first make a sketch of the given problem.

Let h be the hypotenuse.

We need to find sinx and cos x, but to find sinx and cosx, first determine the value of h.

Using the Pythagoras theorem;

hypotenuse² = opposite² + adjacent²

h² = 2² + 3²

h² = 4 + 9

h² =13

Take the square root of both-side of the equation.

h =√13

This implies that hypotenuse = √13

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Using the trigonometric ratio;

\sin x=\frac{opposite}{\text{hypotenuse}}=\frac{2}{\sqrt[]{13}}\cos x=\frac{adjacent}{\text{hypotenuse}}=\frac{3}{\sqrt[]{13}}

And we know that tanx =2/3

From the trigonometric identity;

sin 2x = 2sinxcosx

Substitute the value of sinx , cosx and then simplify.

\sin 2x=2(\frac{2}{\sqrt[]{13}})(\frac{3}{\sqrt[]{13}})=\frac{12}{13}

Hence, sin2x = 12/13

cos2x = cos²x - sin²x

Substitute the value of cosx, sinx and simplify.

\begin{gathered} \cos 2x=(\frac{3}{\sqrt[]{13}})^2-(\frac{2}{\sqrt[]{13}})^2 \\  \\ =\frac{9}{13}-\frac{4}{13} \\ =\frac{5}{13} \end{gathered}

Hence, cos2x = 5/13

tan2x = 2tanx / 1- tan²x

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OR

\tan 2x=\frac{\sin 2x}{\cos 2x}=\frac{\frac{12}{13}}{\frac{5}{13}}=\frac{12}{5}

Hence, tan2x = 12/5

Therefore,

sin2x =12/13

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