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Oxana [17]
3 years ago
14

Find the exact value of the indicated trigonometric function of θ.

Mathematics
1 answer:
Mariana [72]3 years ago
8 0

Answer:

cosθ = -√(35/36)

tanθ = -1/√35

Step-by-step explanation:

We know that

sin²θ + cos²θ = 1

(1/6)² + cos²θ = 1

1 - (1/6)² = cos²θ

35/36 = cos²θ

sec θ = 1/ cosθ

1/ secθ = cos θ

Because secθ < 0, 1/ secθ would also be < 0, so cos θ < 0

cosθ = -√(35/36)

tanθ = sinθ/cosθ = (1/6)/-√(35/36)

= (1/6) / -(√35/6)

= -1/√35

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3 years ago
e vertices of a rectangle are R(-5,-5), S(-6,-5),T(-1,1),U(-5,1) a translation maps R to the point (2,-9)
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Answer:

The rule of translation : (x,y)\rightarrow (x+7,y-4)

The vertices of image is R'(2,-9), S'(1,-9), T'(6,-3) and U'(2,-3).

Step-by-step explanation:

The vertices of a rectangle are R(-5,-5), S(-6,-5), T(-1,1), U(-5,1).

It is given that a translation maps R to the point (2,-9).

Difference between x-coordinates:

-5-2=-7

Difference between y-coordinates:

-5-(-9)=-5+9=4

The x-coordinate increased by 7 and y-coordinate decreased by 4. It means the figure shifts 7 units right and 4 units down.

The rule of translation is

(x,y)\rightarrow (x+7,y-4)

The vertices of image are

R(-5,-5)\rightarrow R'(-5+7,-5-4)=R'(2,-9)

S(-6,-5)\rightarrow S'(-6+7,-5-4)=S'(1,-9)

T(-1,1)\rightarrow T'(-1+7,1-4)=T'(6,-3)

U(-5,1)\rightarrow U'(-5+7,1-4)=U'(2,-3)

Therefore, the vertices of image are R'(2,-9), S'(1,-9), T'(6,-3) and U'(2,-3).

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3 years ago
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Answer:

C/2pi = r

Step-by-step explanation:

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Answer:

x = - 15

Step-by-step explanation:

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Multiply through by 3 to clear the fraction

4x + 9 = 3x - 6 ( subtract 3x from both sides )

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6 0
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3 years ago
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