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snow_tiger [21]
2 years ago
7

Please help me thanks

Mathematics
1 answer:
Mekhanik [1.2K]2 years ago
6 0

Answer:

x=37.74^{0}

Step-by-step explanation:

Let's use the sine law to calculate x.

\frac{x}{sin(90)}=\frac{20}{sin(32)}\\x=\frac{20}{sin(32)}\\x=37.74

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Given: cos θ=-4/5, sin x = -12/13, θ is in the third quadrant, 
USPshnik [31]

By definition of tangent,

tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)

Recall the double angle identities:

sin(2<em>θ</em>) = 2 sin(<em>θ</em>) cos(<em>θ</em>)

cos(2<em>θ</em>) = cos²(<em>θ</em>) - sin²(<em>θ</em>) = 2 cos²(<em>θ</em>) - 1

where the latter equality follows from the Pythagorean identity, cos²(<em>θ</em>) + sin²(<em>θ</em>) = 1. From this identity we can solve for the unknown value of sin(<em>θ</em>):

sin(<em>θ</em>) = ± √(1 - cos²(<em>θ</em>))

and the sign of sin(<em>θ</em>) is determined by the quadrant in which the angle terminates.

<em />

We're given that <em>θ</em> belongs to the third quadrant, for which both sin(<em>θ</em>) and cos(<em>θ</em>) are negative. So if cos(<em>θ</em>) = -4/5, we get

sin(<em>θ</em>) = - √(1 - (-4/5)²) = -3/5

Then

tan(2<em>θ</em>) = sin(2<em>θ</em>) / cos(2<em>θ</em>)

tan(2<em>θ</em>) = (2 sin(<em>θ</em>) cos(<em>θ</em>)) / (2 cos²(<em>θ</em>) - 1)

tan(2<em>θ</em>) = (2 (-3/5) (-4/5)) / (2 (-4/5)² - 1)

tan(2<em>θ</em>) = 24/7

4 0
3 years ago
Write 0.27 as a fraction
aniked [119]
The answer is: 27/100
4 0
3 years ago
Read 2 more answers
3. Find the midpoint between the following points. (-2,-5) and (-3,1) ​
Vadim26 [7]

Answer:

Step-by-step explanation:

(x₁, y₁) = (-2 , -5)   & (x₂ , y₂) = (-3 , 1)

Midpoint = (\frac{x_{1}+x_{2}}{2},\frac{y_{1}+y_{2}}{2})

          =(\frac{-2 + [-3]}{2} ,\frac{-5 + 1}{2})\\\\\\=(\frac{-5}{2} , \frac{-4}{2})\\\\=(-2.5, -2)

7 0
3 years ago
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