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

Answers

Answer 1

Answer:

cosФ = [tex]\frac{1}{\sqrt{65}}[/tex] , sinФ = [tex]-\frac{8}{\sqrt{65}}[/tex] , tanФ = -8, secФ = [tex]\sqrt{65}[/tex] , cscФ = [tex]-\frac{\sqrt{65}}{8}[/tex] , cotФ = [tex]-\frac{1}{8}[/tex]

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 = [tex]\frac{x}{r}[/tex]sinФ = [tex]\frac{y}{r}[/tex]tanФ = [tex]\frac{y}{x}[/tex]secФ = [tex]\frac{r}{x}[/tex]cscФ = [tex]\frac{r}{y}[/tex]cotФ = [tex]\frac{x}{y}[/tex]Where r = [tex]\sqrt{x^{2}+y^{2} }[/tex] (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 = [tex]\sqrt{x^{2}+y^{2} }[/tex]

∵ x = 1 and y = -8

∴ r = [tex]\sqrt{x} \sqrt{(1)^{2}+(-8)^{2}}=\sqrt{1+64}=\sqrt{65}[/tex]

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

∵ cosФ = [tex]\frac{x}{r}[/tex]

∴ cosФ = [tex]\frac{1}{\sqrt{65}}[/tex]

∵ sinФ = [tex]\frac{y}{r}[/tex]

∴ sinФ = [tex]-\frac{8}{\sqrt{65}}[/tex]

∵ tanФ = [tex]\frac{y}{x}[/tex]

∴ tanФ = [tex]-\frac{8}{1}[/tex] = -8

∵ secФ = [tex]\frac{r}{x}[/tex]

∴ secФ = [tex]\frac{\sqrt{65}}{1}[/tex] = [tex]\sqrt{65}[/tex]

∵ cscФ = [tex]\frac{r}{y}[/tex]

∴ cscФ = [tex]-\frac{\sqrt{65}}{8}[/tex]

∵ cotФ = [tex]\frac{x}{y}[/tex]

∴ cotФ = [tex]-\frac{1}{8}[/tex]    


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ryans tennis club Membership Which is 11$ is deducted each month which expression shows the total deductions for the year?

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Answer:

(-$11)x12

Step-by-step explanation:

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In how many ways 50 people can handshake with each other?

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Answer:

My estimate  think it 1225

Step-by-step explanation:

49 / 2 * (49 + 1) = 1225

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along 35 feet of road? *

Answers

Answer:

14 cones

Step-by-step explanation:

20/50=0.4

0.4 times 35=14

Calculate a point estimate of the mean pull-off force of all connectors in the population (Round the answer to four decimal places (e.g. 90.2353).) g

Answers

Answer:

The answer is "75.627"

Step-by-step explanation:

Please find the correct question in the attached file.

The mean displacement force among all connectors throughout the population calculates the point estimation.

[tex]\bold{ \bar x= \frac{\text{Sum of observation}}{\text{Amount of observations}}}[/tex]

   [tex]= \frac{1966.88}{26}\\\\=75.627[/tex]

2x+3y=10 8x+Ay=B
What Is the vaule of B

Answers

X-1/8 b-1/8ay hopefully this helps

How do you find what p is?

Answers

Answer:

p > -3

Step-by-step explanation:

This is an alternating p-series.  It is absolutely convergent if│an│converges.  1 / nᵖ⁺³ converges if the exponent is greater than 1.

p + 3 > 1

p > -2

The series is conditionally convergent if │an│diverges.  1 / nᵖ⁺³ diverges if the exponent is greater than 0 and less than or equal to 1.

0 < p + 3 ≤ 1

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Combining these two, we get p > -3.

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Answers

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B.

Step-by-step explanation:

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Answer:

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Step-by-step explanation:

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divided the input by 3 to get the output

Answers

Answer: that will be 5

Step-by-step explanation:

Answer:

6

Step-by-step explanation:

8 mice.

There are _ mice.
All the mice run away.


_ mice are left.

Please answer correctly

Answers

Answer:

0 because if all the mice ran away then they would be gone

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Answers

Answer: $1.67

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30.06 ÷ 18 = 1.67

The yield in bushels from a grove of orange trees is given by Y = x(600 − x), where x is the number of orange trees per acre. How many trees will maximize the yield?

Answers

Answer:

90000

Step-by-step explanation:

Y = x(600 - x)

Let's rearrange the equation so that we have

Y = x(-x + 600)

Y = -x² + 600

When you take a look at parabolas, we know that their maximum or minimum values are usually on the axis of symmetry. This axis of symmetry has an equation of

x = -b/2a,

In this question, the axis of symmetry is

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This means that planting 300 trees will maximize your yield. If you substitute for x = 300 into the equation, the maximum yield will be

y = 300 (600 - 300)

y = 90000.

Answer: 300

Step-by-step explanation:

use the formula X=-b/2a

x=-600/-2

x=300

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Answers

Answer: so, its pretty simple so just figure it it so, its pretty simple so just figure it it

Step-by-step explanation: so, its pretty simple so just figure it it so, its pretty simple so just figure it it!

which number is the additve inverse of -5

Answers

Answer:

Additive inverses add to 0. The additive inverse of a number is the opposite of the number.

A number, n, is greater than -4 and less than or equal to 6.

Answers

Answer:

-3-,2,-1,0,1,2,3,4,5

Step-by-step explanation:

-4<n<6

What is the y-intercept of the line 3x – 7y = 42?
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What does h(40) = 1700 mean in terms of the problem?
Hours of
Training
10
20
30
40
50
60
70
Monthly
Pay
1250
1400
1550
1700
1850
2000
2150

Answers

Answer:

40 hours of training=h(40)

Monthly Pay=1700

Step-by-step explanation:

For 40 hours of training, you will receive $1700 for the month.

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Answer:

Oiiiiio ka cha thik cha

Write an equation of the line passing through point P(−2, 6) that is parallel to the line x=−5.

Answers

Answer:

x = -2

Step-by-step explanation:

The line x = - 5 means it is a straight vertical line that has no slope. This means that the slope is undefined.

Now, for this line to be parallel to the line passing through point P(−2, 6), it means the line will be a vertical line too with the equation of form (x = a).

Thus, the equation of the line is x = -2

The equation of the line is given by:

[tex]x = -2[/tex]

The equation of a line has the following format:

[tex]y = mx + b[/tex]

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m is the slope, which is the rate of change.b is the y-intercept, which is the value of x when y = 0.If two lines are parallel, they have the same slope.

Line x = -5 is a horizontal line, thus, it's slope is undefined.

A line parallel will also be horizontal, with undefined slope.

It passes through point P(-2,6), thus, the equation of the line is:

[tex]x = -2[/tex]

A similar problem is given at https://brainly.com/question/16302622

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The answer is B. -14*1=-14 and -14+1=-13.
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Mental math what is 90 x 20

Answers

Answer:

1800

Step-by-step explanation:

90*20=1800 because 9*2=18 add two zeroes and ur done

Hope this helps

Answer:

1,800

Step-by-step explanation:

90 x 20

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1,800

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Answers

Answer:

Step 1) 7*7 = 49

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Answer:

Step-by-step explanation:

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The Riley family has 3 children all born 1 year apart. Kate is the youngest, Bradley is the middle child, and Cameron is the oldest. Together, the children's ages total 36. How old is Kate?​

Answers

Step-by-step explanation:

12

Answer:

11

Step-by-step explanation:

11+12+13 =36

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Answers

Wat this doesn’t make sense

A triangle has two sides of length 2 and 15. What compound inequality describes the possible
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Answers

Answer:

13<X<17

Step-by-step explanation:

Triangular Inequalities state that a side is always greater than the absolute value of the difference of the other two sides and less than the sum of the other two sides. You use the inequality |a-b|<c<a+b with a, b, and c as the lengths of the sides.

When you plug in the numbers, (X being c, 2 being b, and 15 being a) you get

|15-2|<X<15+2

|13|<X<17

Which brings us to our final answer of:

13<X<17

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Answers

Answer:

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Answers

Answer:

6. x = 28 degrees

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Step-by-step explanation:

6.  

Notice that you can use the property that tells us that the addition of all internal angles of a triangle must give 180 degrees, then you write the following equation:

50 + 69 + (2 x +5) = 180

combine like terms:

119 + 2 x + 5 = 180

124 + 2 x = 180

subtract 124 from both sides:

2 x = 56

divide by 2 both sides:

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Problem 7.

If the two triangles are congruent, then the side MN must equal side RS.

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and we can write the equation:

1.8 = 3 z - 3

adding 3 to both sides:

1.8 + 3 = 3 z

4.8 = 3 z

dividing both sides by 3:

z = 4.8 / 3

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Answers

1a. Multiply a variable by 13, add 2.

1b. Subtract two from both sides, divide both sides by 13. X=3

2a. Subtract 3 from a variable; divide by 5

2a. Multiply both sides by 5,add 3 to each side. x=-2
Solution (1) :

Solution (a) :

step 1. Multiply the variable x with 13 .

step 2. Add 2 to it .

Solution (b) :

Step 1 : Subtract 2 from both sides : 13x + 2 - 2 = 41 - 2 = 39

Step 2 : Divide both the sides by 13 : 13x ÷ 13 = 39 ÷ 13 = 3

x = 3

Solution (2) :

Solution (a) :

Step 1. Subtract 3 from the variable .

Step 2. Divide the result by 5 .

Solution (b) :

[tex]Step \: 1. \: add\: 3 \: to \: both \: the \: sides : \frac{x - 3}{5} + 3 = - 1 + 3

[/tex]

Step 2 : Multiply both the sides by 5 : 5 × 1/5x = 5 × -2/5

x = -2

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Answers

Answer:

All of the above

Step-by-step explanation:

The answer is b

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Answers

Answer:

7a-5=2a -15

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What’s the difference between m=change in y and change in x and m =y2-y1and x2-x1

Answers

it's the same thing

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