Solve the inequality: 6x+8

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

Pleasee help from anyone

Margaret [11]

Answer:

18 and 22.8 will be your answer

Step-by-step explanation:

4 0

3 years ago

Read 2 more answers

Which correlation coefficient implies that the data points are closest to the line that is used to model the

pochemuha

Answer:

r= 0.87

Step-by-step explanation:

It has the strongest correlation, which means it is closest to the line.

4 0

4 years ago

At leslie's school the ratio of boys and girls is 11 to 12 at marks school the ratio of boys girls is 41 to 48 if both schools h

Softa [21]

Answer: B. There are more boys at Mark's school than at Leslie's school because the ratio 41 to 48 is greater than the ratio 11 to 12.

Step-by-step explanation:

Here are the options:

A There are more boys at Mark's school than at Leslie's school because the ratio 11 to 12 is greater than the ratio 41 to 48.

B. There are more boys at Mark's school than at Leslie's school because the ratio 41 to 48 is greater than the ratio 11 to 12.

C. There are more boys at Leslie's school than at Mark's school because the ratio 41 to 48 is greater than the ratio 11 to 12.

At leslie's school the ratio of boys and girls is 11 to 12. This implies that the fraction of boys in the school to total students will be:

= 11/(11 + 12) = 11/23 = 0.4783

At Marks school the ratio of boys to girls is 41 to 48. Thus implies that the fraction of boys in the school to total students will be:

= 41 / (41 + 48) = 41/85= 0.4824

Based on the calculation, we can deduce that there are more boys at Mark's school than at Leslie's school because the ratio 41 to 48 is greater than the ratio 11 to 12.

6 0

3 years ago

Which measurement could be a perimeter measure? 24.6 in 36 m2 8.5 ml 12 ft3

sergey [27]

It could be the first one or the third the others are not actual measuring units
im going with the first one

7 0

3 years ago

Read 2 more answers

Solve the inequality: 6x+8 > 6(x+2)