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3 years ago

What is the justification for step 1 in the solution process?

Mathematics

1 answer:

Sholpan [36]3 years ago

7 0

It’s the subtraction property of equality because you’re subtracting 15 from both sides

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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

2 years ago

Find the volume of this figure. round your answer to the nearest hundredth. if necessary #8

ivann1987 [24]

Answer:

30 miles²

Step-by-step explanation:

To solve the area of the prism we have to multiply the area of the base * the height of the prism. The base of the prism is a right triangle.

(b*h)÷2 = Area of a triangle

Base = 4

Height = 3

Now:

(4*3)/2 = 6 miles²

Now we have to multiply 6 miles² by 5 as our height.

We get 30 miles² as the volume of the figure.

4 0

2 years ago

What is the equation of the line that is parallel to y-3x=2 and that passes through (6,1)?

Rudik [331]

Slope-intercept form: y = mx + b

(m is the slope, b is the y-intercept or the y value when x = 0 --> (0, y) or the point where the line crosses through the y-axis)

For lines to be parallel, they need to have the same slope.

y - 3x = 2 Add 3x on both sides to change the equation to slope-intercept form

y - 3x + 3x = 2 + 3x

y = 3x + 2 The slope is 3, so the parallel line's slope is also 3.

Now that you know the slope, substitute/plug it into the equation

y = mx + b

y = 3x + b To find "b", plug in the point (6, 1) into the equation, then isolate/get the variable "b" by itself

1 = 3(6) + b

1 = 18 + b Subtract 18 on both sides to get "b" by itself

1 - 18 = 18 - 18 + b

-17 = b

y = 3x - 17 Your answer is the 1st option

8 0

3 years ago

Read 2 more answers

Please answer this thank you

exis [7]

Step-by-step explanation:

option 1

option 3

7 0

2 years ago

(HELPPP PLSSS) A group of friends goes out for lunch. The total bill, excluding tax, is $22. IF tax on the meal is 6% and if a 2

Over [174]

Answer:

22*1.06 = cost of meal with tax = 23.32

22*.20 = tip on the pre-tax cost = 4.40

Total = $27.72

Step-by-step explanation:

8 0

3 years ago

Read 2 more answers