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3 years ago

can someone show me step by step this one too? it says I have to solve for the indicated variable plz help

Mathematics

1 answer:

bearhunter [10]3 years ago

5 0

(a/b)=c
first multiply both sides by b
b*(a/b)=c*b
this cancels out the b under the a
a=cb
Then divide by c
a/c=(cb)/c
this cancels the c and leaves b by itself
b=(a/c)

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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

Given that f(1)=2 and f'(1)=4, find the derivative of f(x)loge(x) when x=1

inessss [21]

Answer:

Step-by-step explanation:

loge(x) is ln(x)

f(x) × ln(x)

Differentiate using product law

[ln(x) × f'(x)] + [(1/x) × f(x)]

x = 1

[ln(1) × f'(1)] + [(1/1) × f(1)]

(0 × 4) + (1 × 2)

0 + 2

3 0

3 years ago

Is 7/9 greater then 8/9

maksim [4K]

No because 7/9= 0.777777777789 and 8/9= 0.888888888888889

6 0

3 years ago

Help super important

const2013 [10]

Hello.

Taking a look at our screenshot provided, we can conclude that we need to find the missing angle degree out of 90 degrees, as we are dealing with a right angle.

Let's set this up as an Algebraic formula and solve for the variable;
5x + 15 + 50 = 90

First, let's combine like-terms (15 and 50).

5x + 65 = 90

Now, isolate our variable by subtracting 65 from each side of the equation.

90 - 65 = 25
65 - 65 = 0

5x = 25

Now, divide both sides by 5 to solve for x, our missing angle degree.

x = 5

Your answer is A.) 5

I hope this helps!

3 0

3 years ago

I need help with what is 0.09 1/10th of? I would like some one to tell me how I calculate this so I may use it for future math p

Gemiola [76]

One tenth of 90. Because regular 9 is one tenth of 90, so decimal 9 is one tenth of decimal 90. Hope you understand ha ha ^_^

5 0

3 years ago