The terminal side of an angle θ in standard position passes through the point (3, 1). Calculate the exact values of the six trig functions for angle θ.

Answers

Answer 1

Answer:

sin α = [tex]\frac{y}{r}[/tex] = [tex]\frac{1}{\sqrt{10} }[/tex]

cos α = [tex]\frac{x}{r}[/tex] = [tex]\frac{3}{\sqrt{10} }[/tex]

tan α = [tex]\frac{y}{x}[/tex] = [tex]\frac{1}{3}[/tex]

cot α = [tex]\frac{x}{y}[/tex] = [tex]\frac{3}{1}[/tex]

sec α = [tex]\frac{r}{x}[/tex] = [tex]\frac{\sqrt{10} }{3}[/tex]

csc α = [tex]\frac{r}{y}[/tex] = [tex]\frac{\sqrt{10} }{1}[/tex]

Step-by-step explanation:

If the point is given on the terminal side of an angle, then:

Calculate the distance between the point given and the origin:

r = [tex]\sqrt{x^2+y^2}[/tex]

Here it is: [tex]\sqrt{3^2+1^2}[/tex] = [tex]\sqrt{9+1}[/tex] = [tex]\sqrt{10}[/tex]

So we have:

x = 3

y = 1

r = [tex]\sqrt{10}[/tex]

Now we can calculate all 6 trig, functions:

sin α = [tex]\frac{y}{r}[/tex] = [tex]\frac{1}{\sqrt{10} }[/tex]

cos α = [tex]\frac{x}{r}[/tex] = [tex]\frac{3}{\sqrt{10} }[/tex]

tan α = [tex]\frac{y}{x}[/tex] = [tex]\frac{1}{3}[/tex]

cot α = [tex]\frac{x}{y}[/tex] = [tex]\frac{3}{1}[/tex]

sec α = [tex]\frac{r}{x}[/tex] = [tex]\frac{\sqrt{10} }{3}[/tex]

csc α = [tex]\frac{r}{y}[/tex] = [tex]\frac{\sqrt{10} }{1}[/tex]


Related Questions

write 0.000046 in scientific notation ​

Answers

The answer would be 4.6 x 10^-5

Hello there! :)

Numbers in scientific notation look like this:

____x10^-

The coefficient must be between 1 and 10:

4.6x10^-

Now,the exponent is how many units we move the decimal place.

The exponent for this number is negative because the number is small.

We move the decimal point 5 times to the left.

Therefore, 0.000046 in scientific notation looks like so:

4.6x10^-5

Hope it helps.

~A lonely teen who helps others with a smile

-Grace :-)

Good luck.

can someone help with this​

Answers

Answer:

A: 9x = 0

Step-by-step explanation:

Description of it's end behavior as * Gets larger 8. Match each rational function with a larger. The value of the expression gets A.9x closer and closer to 0. : 2, The value of the expression gets closer and closer to 1. 2 3. The value of the expression gets 92+ closer and closer to 9. E. 9442 4. The value of the expression is 99 98+2 5. The value of the expression gets larger and larger in the positive direction. 6. The value of the expression gets larger and larger in the negative direction:

What is the value of x in the solution to this system of equations?

y+5x=-1
y=1/2x+32

A. -198/29
B. 29
C. -6
D. 37/33

Answers

Step-by-step explanation:

the answer should be a I think

A triangle has two sides of length 2 and 18. What is the largest possible whole-number length for the third side?

Answers

Answer:

19

Step-by-step explanation:

Given 2 sides of a triangle then the third side x is

difference of 2 sides < x < sum of 2 sides , that is

18 - 2 < x < 18 + 2

16 < x < 20

Then the largest possible length of the third side is 19

solve for x (x-6)^2-5=0

Answers

Answer:

x=6+√5 or x=6−√5

Josh makes a fruit salad with bananas, blueberries, and strawberries. He uses 234 pounds of bananas, 112 pounds of blueberries, and some strawberries. The fruit salad weighs 618 pounds. How many pounds of strawberries does Josh use?

Answers

Answer:

234+112=346

618-346=272

Josh used 272 pounds of strawberries in his fruit salad.

Step-by-step explanation:

Answer:

272

Step-by-step explanation:

Algebra 2 How many Real solutions does the equation have? X-1 squared = x-4

Answers

The solutions are where the lines cross each other.

The lines only cross each other once so there is 1 real solution.

Answer: 1

If anyone reading this is in K12, what state are you in?
I do FL

Answers

Answer:

I am I the state of California

what is the perimeter of 4in. 4in.

Answers

Perimeter = 4 × side

[tex] = 4 \times 4 \\ = 16in[/tex]

The perimeter of a 4-inch square is 16 inches.

56 x 4 + 5 - 53=x
(x) x 23 + 500

Answers

Step-by-step explanation:

56× 4=224

224+5= 229

229-53=176

176×23=4048

4048+500=4548

The answer is = 4548

Rearrange the equation by subtracting what is to the right of the equal sign from both sides of the equation :

56*4+5-53-(x*(x)*x^23+500)=0

Step by step solution :

STEP
1
:

STEP
2
:
Pulling out like terms

2.1 Pull out like factors :

-x25 - 324 = -1 • (x25 + 324)

Equation at the end of step
2
:

-x25 - 324 = 0
STEP
3
:

Solving a Single Variable Equation:

3.1 Solve : -x25-324 = 0

Add 324 to both sides of the equation :
-x25 = 324
Multiply both sides of the equation by (-1) : x25 = -324


x = 25th root of (-324)

Negative numbers have real 25th roots.
25th root of (-324) = 25√ -1• 324 = 25√ -1 • 25√ 324 =(-1)•25√ 324

The equation has one real solution, a negative number This solution is x = negative 25th root of 324 = -1.2601


One solution was found :
x = negative 25th root of 324 = -1.2601

Sally is paid to walk her neighbor’s dog every day.Every month she is paid she puts away $20 and saves the rest.Write an expression that represents the amount she will save in 6 months if she earns m dollars each month.If she’s paid $65 each month how much will she save in 6 months?

Answers

Answer: she would have saved 120$$

Step-by-step explanation:

Can anyone help me please?

Answers

Answer:

ñññ

Step-by-step explanation:

PLEASE ITS DUE 5 MINS

Answers

Answer:

I'm sorry pls retake the pic really quickly.. I can't see the entire problem!

Then I'll add my answer if I can! Thx!

PLEAAAAASSEEEEEEEEEEE
im held captive._.

Answers

The inequality that models the situation is:

[tex]15000 + 4s \geq 450000[/tex]

Solving it, it is found that they need to sell at least 108,750 shirts.

During the day:

They earned 15000 in mask sales.They will sell s shirts, and earn a total of of 4s.

Hence, the earnings are:

[tex]T = 15000 + 4s[/tex]

They want to earn at least 450,000, hence:

[tex]T \geq 450000[/tex]

[tex]15000 + 4s \geq 450000[/tex]

Solving it:

[tex]15000 + 4s \geq 450000[/tex]

[tex]4s \geq 435000[/tex]

[tex]s \geq \frac{435000}{4}[/tex]

[tex]s \geq 108750[/tex]

They need to sell at least 108,750 shirts.

A similar problem is given at https://brainly.com/question/24514895

Solve for x.
2x + 20=2x - 4
+
x = [?]
Enter

Answers

Answer:

x=24

Step-by-step explanation:

2x+20=2x-4+x

Subtract 2x from both sides

2x+20-2x=2x-4+x-2x

Simplify

20=-4+x

Add 4 to both sides

24=x

Switch sides

x=24


At a basketball game, a vender sold a combined total of 161 sodas and hot dogs. The number of sodas sold was 31 more than the number of hot dogs sold. Find
the number of sodas sold and the number of hot dogs sold.

Answers

Answer:

65 hot dogs, 96 sodas

Step-by-step explanation:

x + (x + 31) = 161

2x + 31 = 161

2x = 130

x = 65

65 hotdogs

65 + 31 = 96

96 sodas

can someone please help with this???​

Answers

Answer: Associative property

Answer:

yes

Step-by-step explanation:

its D

Allison buys some cloud storage for her files. On average, she adds files that take up 2​ megabytes each day. After 64​ days, she has 96​ megabytes of memory remaining in the cloud.
Determine the equation, in slope-intercept form, of the line that represents the amount of memory remaining after x​ecks days.

Answers

Answer:

the answer would be a because i had this exact question on ed2020, i think i remember it being A.

Step-by-step explanation:

should be A. hope this helps!!

The LCM of 6, 17 and 34 is

Answers

Answer: 102

Step-by-step explanation:

Can someone please help me with this question

Answers

A. Angle 3 is a vertical angle to angle 2 which means they are the same.

Angle 3 = 76 degrees

B. Angle 6 is also the same as angle 2.

Angle 6 = 76 degrees

C. Angle 8 + angle 6 form a straight line which equals 180 degrees

Angle 8 = 180 - 76 = 104 degrees

Answer:

76° , 76° , 104°

Step-by-step explanation:

(a)

∠ 2 and ∠  3 are vertically opposite angles and are congruent , then

∠ 3 = 76°

(b)

∠ 6 and ∠ 3 are alternate angles and are congruent , then

∠ 6 = 76°

(c)

∠ 6 and ∠ 8 are adjacent angles on a straight line and sum to 180° , then

∠ 8 = 180° - 76° = 104°

Why will nobody answer my questions..

Which graph represents the solution to this inequality?
-1/4(12x+8)<-2x+11

Answers

Answer: I would need a picture of the possible graphs.

Help!! Ill give 100 points if your correct

Answers

[tex]\\ \sf\Rrightarrow 12\dfrac{5}{6}-5\dfrac{1}{6}[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{77}{6}-\dfrac{31}{6}[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{77-31}{6}[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{46}{6}[/tex]

[tex]\\ \sf\Rrightarrow \dfrac{23}{3}[/tex]

[tex]\\ \sf\Rrightarrow 7\dfrac{2}{3}[/tex]

Given info:- Subtract and simplify. 12(5/6) - 5(1/6) The given options are (a) 6(1/3) (b) 5(2/3) (c) 7(1/3) (d) 7(2/3)

Solution: 12(5/6) - 5(1/6)

= (72+5)/6 - (30+1)/6

= 77/6 - 31/6

Take the LCM of 6 and 6 is 6.

so,

= (77*1 - 31*1)/6

= (77-31)/6

= 46/6

= (46÷2)/(6÷2)

= 23/3

= 7(2/3) Ans.

also read similar questions: Add and simplify. 1 1/3 + 2 3/4 A. 3 4/12 B. 3 1/3 C. 3 13/12 D. 49/12 E. 4 1/12 Subtract and simplify. 11 1/12 − 2 2/3 A. 9(−7/12) B. 8 5/12 C. 8 7/12 D. 9 7/1...

https://brainly.com/question/13075467?referrer

Jerome solved the equation 1 3 x + 5 6 = 1 as shown. 1. Subtraction property of equality: 1 3 x + 5 6 − 5 6 = 1 1 − 5 6 2. LCD: 1 3 x = 1 6 − 5 6 3. Multiply by...

https://brainly.com/question/16207685?referrer

-2(x - 3.5) = -2


First step:

Work for first step:

Urgent!!

Second Step:

Work for second step

Value of x:

Answers

X=4.5 is the answer

If my friend answers this question under 5 seconds he's a god

Answers

x = 9

Scale size is 3 so multiply all terms in ABC by 3.

which lines are parallel? how do you know?

Answers

Lines B and C are parallel as they have the same slope

London is deciding between two different movie streaming sites to subscribe to. Plan A costs $9 per month plus $1.50 per movie watched. Plan B costs $38 per month plus $0.50 per movie watched. Let AA represent the monthly cost of Plan A if London watches xx per month, and let BB represent the monthly cost of Plan B if London watches xx movies per month. Write an equation for each situation, in terms of x,x, and determine which plan would be cheaper if London plans on watching 26 movies each month

Answers

Answer:

Plan A is $3 cheaper can Plan B.

Step-by-step explanation:

first equation: 1.5t+9

second equation: .50t+38

Then substiute the 26 for x. So you get 48 for Plan A and 51 for Plan B. Then subtract so you can get 3, for Plan A is three dollars cheaper than Plan B.

Ryan works at a donut shop where he makes $10.25 per hour. He works on at the school bookstore where he makes $8.75 per hour to worked 20 hours last week and made $196, how many hours did he work at each place?

Answers

Step-by-step explanation:

x = hours donuts

y = hours books

x + y = 20

10.25x + 8.75y = 196

from the first equation we get

x = 20 - y

that we use now in the second

10.25×(20 - y) + 8.75y = 196

205 - 10.25y + 8.75y = 196

-1.5y = -9

1.5y = 9

y = 9/1.5 = 6

x = 20 - y = 20 - 6 = 14

he worked 14 hours in the donut shop and 6 hours in the bookstore.

2
Question 7(Multiple Choice Worth 1 points)
(04.04LC)
Point P on the coordinate grid below shows the location of a stage light. A second stage light is 6 units above P. The length of each square on the grid is
2 units. What are the coordinates of the location of the second stage light?
2
16-14-12-1046
012101
O (8.-10)
O (8,2)
(14,2)
(14.-10)

Answers

Answer:

Add 8 to the y value of point p, (4, -2 +8)So the location of the second light is on point (4,6)

Two-Variable Statistics:Question 2

You obtain a correlation value of r = -0.744 when you

analyze the relationship between the time it takes

someone to swim a mile and her heart rate at the end of

the swim. Choose the word completes this interpretation

of the correlation value: The correlation between the time

it takes to swim and heart rate is ___ and ___

Answers

I think it is your second option 5

How do I draw perpendicular line

Answers

Answer:

Follow these steps and you will find how to make a perpendicular line.

Step-by-step explanation:

Open the compass to a radius less than half the segment.

Draw two arcs intersecting the line on both sides of the point.

Draw two arcs using the intersection points as the centers. ...

Construct a line between this point and the original point.

Hope this helped :) -ish

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