How do you simplify the following trigonometric expression:

1 answer:

5 0

$\bf \cfrac{sec(x)sin(x)+cos(\pi -x)}{1+sec(x)}\\\\
-----------------------------\\\\
sec(\theta)=\cfrac{1}{cos(\theta)}\qquad \qquad cos(\pi )=-1\qquad sin(\pi )=0
\\\\
cos({{ \alpha}} + {{ \beta}})= cos({{ \alpha}})cos({{ \beta}})- sin({{ \alpha}})sin({{ \beta}})\\\\
-----------------------------\\\\
\cfrac{\frac{1}{cos(x)}sin(x)+[cos(\pi )cos(x)+sin(\pi )sin(x)]}{1+\frac{1}{cos(x)}}
\\\\\\
\cfrac{\frac{sin(x)}{cos(x)}+[-1\cdot cos(x)+0\cdot sin(x)]}{\frac{cos(x)+1}{cos(x)}}$

$\bf \cfrac{\frac{sin(x)}{cos(x)}+[-cos(x)]}{\frac{cos(x)+1}{cos(x)}}\implies \cfrac{\frac{sin(x)-cos^2(x)}{cos(x)}}{\frac{cos(x)+1}{cos(x)}}
\\\\\\
\cfrac{sin(x)-cos^2(x)}{cos(x)}\cdot \cfrac{cos(x)}{cos(x)+1}\implies \cfrac{sin(x)-cos^2(x)}{cos(x)+1}$

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MariettaO [177]

Answer:

sorry to answer late but..

Step-by-step explanation:

$\frac{1}{75} cm$ = $\frac{scale }{real}$

the wings of the real plane are 12 meters or 1200 cm

we want to solve for the scale, sooo do the algebra...get scale by it self..

real * $\frac{1}{75}$ = scale

1200 * $\frac{1}{75}$ = 16

The scale model wings are 16 cm 2.54 cm is one inch so the wings are approx. 6.3 inches

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2 years ago

Each contestant in the Hunger Games must be trained to compete. Suppose that the time it takes to train a contestant has mean 5

LiRa [457]

Answer:

11.51% probability that it will take less than 450 days to train all the contestants.

Step-by-step explanation:

To solve this question, we need to understand the normal probability distribution and the central limit theorem.

Normal probability distribution

When the distribution is normal, we use the z-score formula.

In a set with mean $\mu$ and standard deviation $\sigma$ , the zscore of a measure X is given by:

$Z = \frac{X - \mu}{\sigma}$

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

Central Limit Theorem

The Central Limit Theorem estabilishes that, for a normally distributed random variable X, with mean $\mu$ and standard deviation $\sigma$ , the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean $\mu$ and standard deviation $s = \frac{\sigma}{\sqrt{n}}$ .