HELP!!!!!plz!!!!!!ASAP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

find the values of the six trigonometric functions for angle theta in standard position if a point with the coordinates (1, -8)

frutty [35]

Answer:

cosФ = $\frac{1}{\sqrt{65}}$ , sinФ = $-\frac{8}{\sqrt{65}}$ , tanФ = -8, secФ = $\sqrt{65}$ , cscФ = $-\frac{\sqrt{65}}{8}$ , cotФ = $-\frac{1}{8}$

Step-by-step explanation:

If a point (x, y) lies on the terminal side of angle Ф in standard position, then the six trigonometry functions are:

cosФ = $\frac{x}{r}$
sinФ = $\frac{y}{r}$
tanФ = $\frac{y}{x}$
secФ = $\frac{r}{x}$
cscФ = $\frac{r}{y}$
cotФ = $\frac{x}{y}$

Where r = $\sqrt{x^{2}+y^{2} }$ (the length of the terminal side from the origin to point (x, y)

You should find the quadrant of (x, y) to adjust the sign of each function

∵ Point (1, -8) lies on the terminal side of angle Ф in standard position

∵ x is positive and y is negative

→ That means the point lies on the 4th quadrant

∴ Angle Ф is on the 4th quadrant

∵ In the 4th quadrant cosФ and secФ only have positive values

∴ sinФ, secФ, tanФ, and cotФ have negative values

→ let us find r

∵ r = $\sqrt{x^{2}+y^{2} }$

∵ x = 1 and y = -8

∴ r = $\sqrt{x} \sqrt{(1)^{2}+(-8)^{2}}=\sqrt{1+64}=\sqrt{65}$

→ Use the rules above to find the six trigonometric functions of Ф

∵ cosФ = $\frac{x}{r}$

∴ cosФ = $\frac{1}{\sqrt{65}}$

∵ sinФ = $\frac{y}{r}$

∴ sinФ = $-\frac{8}{\sqrt{65}}$

∵ tanФ = $\frac{y}{x}$

∴ tanФ = $-\frac{8}{1}$ = -8

∵ secФ = $\frac{r}{x}$

∴ secФ = $\frac{\sqrt{65}}{1}$ = $\sqrt{65}$

∵ cscФ = $\frac{r}{y}$

∴ cscФ = $-\frac{\sqrt{65}}{8}$

∵ cotФ = $\frac{x}{y}$

∴ cotФ = $-\frac{1}{8}$

8 0

3 years ago

Suppose that it is known that the number of items produced in a factory during a week is a random variable with mean 50. If the

iVinArrow [24]

Answer:

The probability would be 0.9586

Step-by-step explanation:

Given,

Mean, $\mu = 50$ ,

Variance, $\sigma^2 = 24$

Standard deviation,

$\sigma = \sqrt{24}=2\sqrt{6}$ ,

If X represents the number of items produced in a factory during a week.

Hence, the probability that this weeks production will be between 40 and 60

$=P(40 < X < 60)$

$=P(\frac{40-\mu}{\sigma} < \frac{X-\mu}{\sigma} < \frac{60-\mu}{\sigma})$

$=P(\frac{40-50}{2\sqrt{6}} < z < \frac{60-50}{2\sqrt{6}})$

$=P(-\frac{10}{2\sqrt{6}} < z < \frac{10}{2\sqrt{6}})$

$=P(-2.041 < z < 2.041)$

$=P(z< 2.041) - P(z< -2.041)$

Using z score table

= 0.9793 - 0.0207

= 0.9586

4 0

3 years ago

Carla drew a picture that was 7/10 of an inch long. Her picture was 0.67 inches wide. Which is greater, the length or width? exp

mr Goodwill [35]

Answer:

width

Step-by-step explanation:

7/10= 7 divided by 10= 0.7

and 0.67 id greater than 0.7

5 0

2 years ago

Sheila walks 1/2 mile in 1/5 hour. What is her unit rate of speed

Trava [24]

Answer:

2 1/2 miles per hour

Step-by-step explanation:

6 0

3 years ago

Read 2 more answers

A company loses $780 as a result of shipping delay the 6 owners of the company must share the loss equally.

tekilochka [14]

A) Change in profit for each owner = -780/8

B) Change in profit for each owner = -$130

The total loss = $780

Number of owners = 6

The 6 owners must share the loss equally

The change in profit for each owner will be the original profit less 780/6

That is -780/6

Evaluating -780/6

Change in profit for each owner = -$130

Learn more here: brainly.com/question/17858380

7 0

3 years ago