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3 years ago

If tan theta = 12/5 and cos theta < 0, what is sin theta ?

1 answer:

8 0

1 + tan ² Ф=sec²Ф
1+(12/5)²=sec²Ф
169/25=sec² Ф
sec Ф=⁺₋√(169/25)=⁺₋13/5

sec Ф=1/cos Ф ⇒cosФ=1/sec Ф
cos Ф>0 ⇔ sec Ф>0 ⇔ sec Ф=+ 13/5

cos Ф=1/secФ
cos Ф=1 / 13/5=5/13

we can calculate the sin Ф, with this method.
sin²Ф + cos²Ф=1 ⇒ sin Ф=⁺₋√(1-cos² Ф)
sin Ф=⁺₋√[1-(5/13)²]=⁺₋12/13
like cos Ф>0 and tan Ф>0 ⇒ sin Ф>0 ⇒sin Ф=12/13

answer: d.12/13

other method
tan Ф=sin Ф / cos Ф
12/5=sin Ф / 5/13
sin Ф=(12/5)*(5/13)=12/13

answer: d.12/13

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Marina86 [1]

Answer:

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Step-by-step explanation:

Data Given:

P = (x,y,z)

Distance from P to A (-3,6,3) = Twice the distance from P to B(6,2,-3)

Solution:

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It is given that:

PA = 2PB

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Solving the above equation:

$(x + 3))^{2}$ + $(y - 6)^{2}$ + $(z-3)^{2}$ = 4 x { $(x-6)^{2}$ + $(y-2)^{2}$ + $(z + 3))^{2}$ }

$x^{2}$ + 9 + 6x + $y^{2}$ + 36 - 12y + $z^{2}$ + 9 - 6z = 4 { $x^{2}$ + 36 - 12x + $y^{2}$ + 4 - 4y + $z^{2}$ + 9 + 6z}

$x^{2}$ + 9 + 6x + $y^{2}$ + 36 - 12y + $z^{2}$ + 9 - 6z = 4 $x^{2}$ + 144 - 48x +4 $y^{2}$ + 16 - 16y + 4 $z^{2}$ + 36 + 24z

Putting the right hand side = 0 and solving the equation:

$x^{2}$ - 4 $x^{2}$ + $y^{2}$ - 4 $y^{2}$ + $z^{2}$ - 4 $z^{2}$ + 6x + 48x - 12y +16y -6z - 24z + 9 + 36 + 9 -144 - 16 - 36 = 0

-3 $x^{2}$ - 3 $y^{2}$ -3 $z^{2}$ + 54x + 4y -30z -142 = 0

Taking (-) common

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3 $x^{2}$ + 3 $y^{2}$ + 3 $z^{2}$ - 54x - 4y +30z + 142 = 0

dividing the whole equation by 3

$x^{2}$ + $y^{2}$ + $z^{2}$ - 54/3x - 4/3y +30/3z + 142/3 = 0

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3 years ago

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nata0808 [166]

Answer:

2.2 or 11/5

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3 years ago

Write and solve an equation to find your final score. Use x to represent your final score.

attashe74 [19]

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2 years ago

Find the circumference of a circle with an area of 615.75 square inches.

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3 years ago

Gina is a certain age (g). Gina's older sister is twice Gina's age. Gina's brother is half Gina's age. The sum of their ages is

aliina [53]

Answer:

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Step-by-step explanation:

First, we will have to write these statements mathematically and then solve.

Let Gina's age be x, let Gina's brother's age be y and let Gina's sister's age be z.

The second statement"Gina's older sister is twice Gina's age" can be mathematically written as: z =2 x ---------------------------(1)

The next statement "Gina's brother is half Gina's age" can be mathematically written as y = $\frac{x}{2}$ ---------------------------------------(2)

Then the next statement "the sum of their ages is 42" can be mathematically written as: x + y + z = 42 ----------------------------(3)

We can now proceed to solve;

Substitute equation (1) and equation(2) into equation (3)

x + y + z = 42

x + $\frac{x}{2}$ + 2x = 42

Multiply through by 2

2x + x + 4x = 84

7x = 84

Divide both-side of the equation by 7

$\frac{7x}{7}$ = $\frac{84}{7}$

x = 12

Therefore, Gina is 12 years old

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3 years ago