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ch4aika [34]
2 years ago
12

Rewrite each expression in terms of sine and cosine only.

Mathematics
1 answer:
Sliva [168]2 years ago
6 0

Answer:

1. Cosθ / SineθCosθ

2. Sineθ / Cos²θSineθ

3. Cosθ / Sineθ

4. Cos²θ + Sin²θ – Sin²θ

Step-by-step explanation:

1. SecθCotθ

Recall

Sec θ = 1/Cos θ

Cot θ = 1/Tan θ

But Tan θ = Sine θ / Cos θ

Thus,

Cot θ = 1 ÷ Sine θ / Cos θ

Cot θ = 1 × Cos θ / Sine θ

Cot θ = Cos θ / Sine θ

Therefore,

SecθCotθ = 1/Cos θ × Cos θ / Sine θ

SecθCotθ = Cosθ / SineθCosθ

2. SecθTanθCscθ

Recall

Sec θ = 1/Cos θ

Tan θ = Sine θ / Cos θ

Csc θ = 1/Sine θ

Thus,

SecθTanθCscθ =

1/Cosθ × Sineθ/Cosθ × 1/Sineθ

= Sineθ / Cos²θSineθ

3. Cscθ/Secθ

Recall

Csc θ = 1/Sine θ

Sec θ = 1/Cos θ

Thus,

Cscθ/Secθ = 1/Sine θ ÷ 1/Cos θ

= 1/Sine θ × Cos θ

= Cosθ / Sineθ

4. Cosθ / Secθ

Recall

Sec θ = 1/Cos θ

Cosθ / Secθ = Cosθ ÷ 1/Cosθ

= Cosθ × Cosθ

= Cos²θ

Recall

Cos²θ + Sin²θ = 1

Cos²θ = 1 – Sin²θ

But

1 = Cos²θ + Sin²θ

Thus,

Cos²θ = Cos²θ + Sin²θ – Sin²θ

Therefore,

Cosθ / Secθ = Cos²θ + Sin²θ – Sin²θ

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Accrotime is a manufacturer of quartz crystal watches. Accrotime researchers have shown that the watches have an average life of
kirza4 [7]

Answer:

a

   P(X <  24 )=  21.186\%  

b

    x =  19.78 \  months

Step-by-step explanation:

From the question we are told that

 The mean is   \mu  =  26 \  months

 The standard deviation is  \sigma  =  4 \  months

 Generally 2 year is  equal to  24 months

Generally the percentage of total production will the company expect to replace is mathematically represented as

      P(X <  24 )=  P(\frac{X - \mu }{ \sigma} <  \frac{24 - 26}{4}  )

Generally  \frac{X - \mu}{\sigma } =Z (The  \ standardized \  value  \  of  \  X )

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Generally from the z-table  

       P(Z <  -0.8) =  0.21186

So

       P(X <  24 )=  0.21186

Converting to percentage

      P(X <  24 )=  0.21186  * 100

=>    P(X <  24 )=  21.186\%  

Generally the duration that should be the guarantee period if  Accrotime does not want to make refunds on more than 6% is mathematically evaluated as

    P(X <  x) =  P(\frac{X - \mu }{\sigma}  < \frac{x - 26}{4} )= 0.06

=> P(X <  x) =  P(Z < \frac{x - 26}{4} )= 0.06

From the normal distribution table the z-score for  0.06 at the lower tail  is

       z = -1.555

So

    \frac{x - 26}{4} = -1.555

=> x =  19.78 \  months  

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3 years ago
11.25 for 2/3 pound how much per pound?
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Divide 11.25 by (2/3). The answer is 16.875
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Consider the given density curve.
alisha [4.7K]

The Median of the density is -6.

An illustration of a numerical distribution with continuous results is a density curve. A density curve is, in other words, the graph of a continuous distribution. This implies that density curves can represent continuous quantities like time and weight rather than discrete events like rolling a die (which would be discrete). As seen by the bell-shaped "normal distribution," density curves either lie above or on a horizontal line (one of the most common density curves).

It is clearly visible from the uniform density curve given in the question that the median of the population density is  -6.
Because the area to the left and right of the density curve is the same.

Hence, the Median of density is -6.

Learn more about density curves here-

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ANTONII [103]
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