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3 years ago

Rewrite the expression as an equivalent expression that does not contain powers of trigonometric functions greater than 1.

Mathematics

1 answer:

Gnesinka [82]3 years ago

6 0

Cos^4(x) =
(cos²x)² =
(1-sen²x)² =
1² - 2*1*sen²x + sen^4x =
1 - 2sen²x + sen^4x

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The table represents the observed number of leaves y on x branches of a tree. Calculate the rate of change between 3 and 4 branc

Dennis_Churaev [7]

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Step-by-step explanation:

The rate of change of number of tree y on x branches of a tree is expressed as shown;

m = Δy/Δx where;

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Δx is change in number of branches between 3 and 4

m = Δy/Δx = y₂-y₁/x₂-x₁

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3 years ago

Two points in the Cartesian plane are A(2.00 m, −4.00 m) and B(−3.00 m, 3.00 m). Find the distance between them and their polar

Brrunno [24]

The distance between the two points is $d=8.6m$

The polar coordinate of A is $\left(4.47,296.57\right)$

The polar coordinate of B is $\left(4.24,135\right)$

Explanation:

The two points are $A(2,-4)$ and $B(-3,3)$

The distance between two points is given by,

$d=\sqrt{(2+3)^{2}+(-4-3)^{2}}\\d=\sqrt{(5)^{2}+(-7)^{2}}\\d=\sqrt{25+49}\\d=8.6$

Thus, the distance between the two points is $d=8.6m$

The polar coordinates of A can be written as $(Distance, tan^{-1} \frac{y}{x} )$

Distance = $\sqrt{x^{2} +y^{2} }$

Substituting $A(2,-4)$ , we get,

Distance = $\sqrt{2^{2} +(-4)^{2} }=\sqrt{4+16 }=4.47$

$tan^{-1} \frac{y}{x} =tan^{-1} \frac{-4}{2}=-63.43$

To make the angle positive, let us add 360,

$\theta=360-63.43=296.57$

The polar coordinate of A is $\left(4.47,296.57\right)$

Similarly, The polar coordinate of B can be written as $(Distance, tan^{-1} \frac{y}{x} )$

Distance = $\sqrt{x^{2} +y^{2} }$

Substituting $B(-3,3)$ , we get,

Distance = $\sqrt{(3)^{2}+(3)^{2}}=4.24$

$tan^{-1} \frac{y}{x} =tan^{-1} \frac{3}{-3}=-45$

To make the angle positive, let us add 360,

$\theta=180-45=135^{\circ}$

The polar coordinate of B is $\left(4.24,135\right)$

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3 years ago