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]    


Related Questions

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

Answers

Answer:

(-$11)x12

Step-by-step explanation:

hope this helps if its right can i get brainliest

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

Answers

Answer:

My estimate  think it 1225

Step-by-step explanation:

49 / 2 * (49 + 1) = 1225

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

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

x = -600 / -2

x = 300

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

subtract 8 from the input to get the output
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:

What is the y-intercept of the line 3x – 7y = 42?
(0, -6)
(-6, 0)
(0, 14)
(14, 0)
please dont jus put something random i will report it.

Answers

The answer is (0,-6)

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.

BI
Challenge 2
A: Can you find the
area of the circle?
r=x +1
B: Can you find the
circumference of
the circle?

Answers

Answer:

Area of the circle = pi * r^2 = pi * (x+1) ^ 2

Circumference of the circle = 2* pi * r = 2*pi*(x+1)

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.

At Sakaro's Sushi, you can get 18 wraps for $30.06 What is the price for 1 wrap?

Answers

Answer: $1.67

Let's make an equation for the problem. To find the price for each sushi roll, divide the price by the number of sushi rolls.

30.06 ÷ 18 = 1.67

I'm still figure is a rectangular prism identity which one of the line segment in the given figure is perpendicular to HG​

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!

I NEED HELP PLEASE AND SHOW THE WORK PLEASE

Answers

Answer:

6. x = 28 degrees

7.  z = 1.6 cm

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:

x = 56 / 2

x = 28 degrees

Problem 7.

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

Since MN  measure 1,8 cm, then RS must also measure 1.8 cm

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

z = 1.6 cm

3. At a road work site, 20 cones are placed along 50 feet of road. How many cones are placed
along 35 feet of road? *

Answers

Answer:

14 cones

Step-by-step explanation:

20/50=0.4

0.4 times 35=14

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

-3 < p ≤ -2

Combining these two, we get p > -3.

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

So  Kate would be 11. Bradley would be 12. And Cameron would be 13

Can someone please help me I need help and I can’t understand this plsssss

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

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]

In which:

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

7 x7 dived by 5 plz helppppvme

Answers

Answer:

Step 1) 7*7 = 49

Step 2)  49/5 = 9.8

Answer:

Step-by-step explanation:

7x7=49, 49 divided by 5=9.8, hope I helped! :P

Solve the following equation: 7a-5=2a-15

Answers

Answer:

7a-5=2a -15

7a-2a=-15+5

5a=-10

5a/5=-10/5

a=-2

What is the answer to this problem

Answers

Answer:

All of the above

Step-by-step explanation:

The answer is b

Hope this helps

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:

B.

Step-by-step explanation:

They are used to the climate and they are harder the the rest.

Answer:

dry climate or

Step-by-step explanation:

they are in wet climate

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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x+12x-13 = 0 and azo, what
is the value x+lo?​

Answers

Wat this doesn’t make sense

A triangle has two sides of length 2 and 15. What compound inequality describes the possible
lengths for the third side, X?

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

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]

Due today HELP PLEASEEEEE!!!

Answers

Answer:

Oiiiiio ka cha thik cha

HELP URGENT !!!!!!!!!!!

Answers

The answer is B. -14*1=-14 and -14+1=-13.
I believe the answer is B. Please correct me if I’m wrong! Good luck!

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

9 x 2=18

18+00

1,800

Plz give Brainiest

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