solve the trigonometric function
tan∅ × sin∅ × cos∅ + cos2∅

Answers

Answer 1

Answer:

cos²Θ

Step-by-step explanation:

simplify the expression using the identities

tanΘ = [tex]\frac{sin0}{cos0}[/tex]

cos2Θ = 1 - 2sin²Θ

cos²Θ = 1 - sin²Θ

then

tanΘ × sinΘ × cosΘ + cos2Θ

= [tex]\frac{sin0}{cos0}[/tex] × sinΘ × cosΘ + 1 - 2sin²Θ ( cancel cosΘ on numerator/ denominator )

= sinΘ × sinΘ + 1 - 2sin²Θ

= sin²Θ + 1 - 2sin²Θ

= 1 - sin²Θ

= cos²Θ

Answer 2

Answer:

[tex]\cos^2(\theta)[/tex]

Step-by-step explanation:

Trig identities used:

[tex]\cos(2\theta)=\cos^2(\theta)-\sin^2(\theta)[/tex]

[tex]\tan(\theta)=\dfrac{\sin(\theta)}{\cos(\theta)}[/tex]

Therefore,

[tex]\tan(\theta)\times\sin(\theta)\times\cos(\theta)+\cos(2\theta)[/tex]

[tex]=\dfrac{\sin(\theta)}{\cos(\theta)}\times\sin(\theta)\times\cos(\theta)+\cos(2\theta)[/tex]

[tex]=\sin^2(\theta) +\cos(2\theta)[/tex]

[tex]=\sin^2(\theta) +\cos^2(\theta)-\sin^2(\theta)[/tex]

[tex]=\cos^2(\theta)[/tex]


Related Questions

find a line that is parallel to y= 8x+10 and has a y intercept of 5

Answers

To be parallel it needs the same slope which is 8x. Now just replace the + 10 with the given y intercept.


Answer y = 8x -5

Answer:

y = 8x -5

Step-by-step explanation:

Need help doing this

Answers

Answer:

9x - 115°

Step-by-step explanation:

Hope this helps!

If not I am sorry.

i could be wrong

Confused need some quick help

Answers

Answer:

B. 8

Step-by-step explanation:

simply just plug the possible answers into the equation for x. plugging in 7 comes out to 39, or one short, so 8 is the answer because the question asks for the fewest ads to run to get the 40 customer goal

Answer:

B;  8

Step-by-step explanation:

4(8) +11 is the least amount of ads youd have to buy to acquire 40 new customers

Round each fraction to the nearest half to find the estimate. There is eight tenths of a cake and Riley eats six tenths of it. Estimate how much cake is left. Explain your thinking.

Answers

Answer:

2/10 or 1/5

Step-by-step explanation:

take 6 away from 8 and you get 2. That is your numerator. If you had 10 to begin with, that is your denominator so it will look like 2/1. IF SIMPLIFIED IT IS 1/5.

Answer:

2/10 or 1/5

Step-by-step explanation:

8/10-6/10=2/10

If fractions have the same number on the bottom, you can subtract or add the top numbers. The bottom number does not change during this process.

Please help 40 points
Step by step show the explanation

Answers

Answer:

i simplify

Step-by-step explanation:

Need help with this question

Answers

Answer:

About 3%

Step-by-step explanation:

It decreased.

3% of 465056=13951

465056-13951=451105

3.6% of 465056=16742

465056-16742=448314

The amount you want it 450678 and 451105 is closer to 450678 than 448314.

Based on the diagram below, what is the interior measure of ∠Y ?

Answers

Answer:

∠Y = 104°

Step-by-step explanation:

vertical angles are equal ⇒ ∠DAN = ∠SAY = 48°

Sum of interior angles of a triangle = 180°

⇒ ∠SYA + 56 + 48 = 180

⇒ ∠SYA = 76°

Angles on a straight line add up to 180°

⇒ ∠Y + ∠SYA = 180°

⇒ ∠Y + 76 = 180

⇒ ∠Y = 104°

i suck with these type of problems please help

Answers

Answer:

Step-by-step explanation:

[tex]tan \ 64 =\dfrac{opposite \ side}{adjacent \ side}\\\\2.05=\dfrac{x}{11}\\\\2.05*11=x\\\\\\x = 22.55[/tex]

A group of students organized a car wash to raise money for a local charity. The students charged $9.99 for each car they watched. In 3.5 hours they washed 14 cars.at that rate how much money could they earn in 8 hours?

Answers

Answer:

$319.68

Step-by-step explanation:

1. 14*9.99=139.86

2. 139.86/3.5=39.96

3. 39.96*8=319.68

Hope this helps

They made 314 washing cars making 9.99 a car

What the answer?? .................?.?.?

Answers

i mean i also like pizza in California

Whitch statement is true?

A The greates common factor of 10 and 14 is 5.
B The greatest common factor of 10 and 15 is 5.
C The greatest common factor of 13 and 21 is 3.
D The greatest common factor of 14 and 21 is 3.​

Answers

B. The greatest common factor of 10 and 15 is 5

Hi There!

The greatest common factor of 10 and 14 is 5 [FALSE]The greatest common factor of 10 and 15 is 5. [TRUE]The greatest common factor 13 and 21 is 3. [FALSE]The greatest common factor of 14 and 21 is 3. [FALSE]Step-by-step explanation:A factor is a number that a number can be evenly divisible by.Example: 5 is a factor of 10, because 10 can be evenly divided by 5.Example #2: 3 is not a factor of 13, because 13 is a prime number, which means it has only 2 factors - 13 and 1.3 is not a factor of 14. The factors of 14 are: 1, 2, 7, 14.5 is not a factor of 14 (reason - above)Hope it helps!

Have an awesome day!

[tex]\huge\text{\bf{TheStarryNights}}[/tex]  :):)

all the students in the six grade either purchased their lunch or brought their lunch from home on monday. 24% of the students purchased their lunch. 190 students brought their lunch from home how many students are in the six grade

Answers

Answer:

190 students = 76%

1% = 190 / 76 = 2.5

24% = 24 * 2.5 = 60 students

190 + 60 = 250 students

Beatrice has at least one quarter, one dime, one nickel, and one penny. She has exactly 13 coins total. Beatrice also has a total value of 92 cents. How many different sets of coins can she have?

Answers

Answer:

(Q, D, N, P) = (0, 7, 4, 2) or (1, 3, 7, 2)

Step-by-step explanation:

Let the numbers of coins be Q, D, N, P

We have:

Q + D + N + P = 13

25Q + 10D + 5N + P = 92

Obviously, P = 2, so

Q + D + N = 11         (1)

25Q + 10D + 5N = 90

Divide by 5 and get

5Q + 2D + N = 18      (2)

(2) - (1), get

4Q + D = 7

Let D = 7, Q = 0, from (1), N = 4, so the set is (Q, D, N, P) = (0, 7, 4, 2)

Let D = 3, Q = 1, from (1), N = 7, so the set is (Q, D, N, P) = (1, 3, 7, 2)

If D = 6, 5, 4, 2, 1, 0, Q is not an integer, these can be ignored.

Harshpreet is at Bowl 360 and is walking towards John
Adams High School. What can be a possible location that is
above his path?

Answers

Answer:

near 1075 m distance

Step-by-step explanation:

the photo is not clear

which one of the following is an integer to -1 and 0.​

Answers

Answer:

-1 is an integer 0 is a whole number

hich two mathematical operations use the commutative property?

multiplication and subtraction.
subtraction and addition.
division and multiplication.
multiplication and addition.

Answers

Answer:

Step-by-step explanation:

multiplication:)

Answer:

The commutative property works only with addition and multiplication because when you change the order of them, the answer wouldn't change.

the price of an item has risen to $240 today. Yesterday it was $120 . Find the percentage increase.

Answers

Answer:

100% increase

Step-by-step explanation:

240/120*100=2*100=200

200-100=100

You go to the store to buy a new TV that is $430. If the tax is 6% of that price, what is the total cost of the TV including tax?

Answers

Answer:

$455.8

Step-by-step explanation:

6% of 430 = 25.8

430 + 25.8 = 455.8

If you need further help, let me know.

- profparis

Answer:

$455.80

Step-by-step explanation:

Given the following question:

6% of 430

To find the answer we must first use the formula to calculate percentages to find 6% of 430. Then we add that answer to the initial price of the TV to have our final answer.

[tex]\frac{p\times n}{100}[/tex]
[tex]\frac{6\times430}{100}[/tex]
[tex]6\times430=2580[/tex]
[tex]2580\div100=25.8[/tex]
[tex]=25.80[/tex]

Now add the answer to the initial price of the TV:
[tex]430[/tex]
[tex]430+25.80=455.8[/tex]
[tex]=455.80[/tex]

The cost of the TV after a 6% tax is "$455.80."

Hope this helps.

3/8 of the students in the class play have names that begin with M what fraction of the students in the play have names that do not begin with M?

Answers

Answer: 5/8

Step-by-step explanation:

This fraction is talking about a whole, so 3/8 + x = 1.

Knowing this, we just do 1 - 3/8, which is 5/8.

The directions on a turkey tell you to cook the turkey 20 minutes per pound.
Part A: Write a function in function notation for this situation where X is the number of pounds.
Part B: Describe the domain of this function. Assume turkeys can weigh up to 30 pounds.
Part C: Graph this function and state the range.
Part D: Use this graph to determine the cooking time for an 18 pound turkey.

Answers

Answer:

Step-by-step explanation:

Let y be the time required to cook the turkey, and x the number of pounds of the turkey.

The time required, x, is equal to the turkey's weight (in lbs) times 20 min/lb.

y = 20(min/lb)x

The domain of this function is 0 - 30 pounds.

The cook time for an 18 lb turkey is y = (20min/lb)*(18 lb) = 360 min

See the attached image.

Pleaae help, have nice day/night!​

Answers

Answer:

I did the whole thing

Step-by-step explanation:

How you do them is you just take each number, and multiply by the number that both fractions can multiply into. I showed how in the picture.

Answer:

1.23

30

2.24

35

3.25

36

4.11

10

5.13

14

6.662

1143

7.19

15

8.11

12

Step-by-step explanation:

tama po ba answer ko

Suzanna lays the books end to end and finds that the board is the same length as 21 books. How many centimeters long is the board?

pls use step by step ty​

Answers

Answer:

Step-by-step explanation:

80 points!!!!!!!

Kay's gross pay is $2,851. Her deductions total $491.22. What percent of her gross pay is take-home pay?

Show work for 80 points!!!!

Answers

Answer:

Her take home pay is $2359.78

The percentage is approximately 82.77%

Step-by-step explanation:

Gross is the full before tax or whatever.

$2851 - $491.22 = $2359.78

$2359.78 / $2851 = 0.827702

$2851 - $491.22 = $2359.78

$2359.78 / $2851 = 0.827702

so the answer is 0.827702

Can someone plsss help me with this question??

thank you very muchh!!!

Answers

Answer:

1 can of fruit A and 1 can of Fruit B

Step-by-step explanation:

3 + 1 : 5 + 4

= 4 : 9

Answer:

1 can of juice A + 1 can of juice B

Step-by-step explanation:

Juice A

mango : strawberry = 3 : 5

Juice B

mango : strawberry = 1 : 4

Juice C

mango : strawberry = 4 : 9

⇒ 1 can of juice A + 1 can of juice B = 3 + 1 : 5 + 4 = 4 : 9

Find the perimeter of this triangle

Answers

The answer to the question is 6x+10 as below shows the steps in solving the problem

PLEASEEEE HELP I NEED A ANSWER ASAP!!!!!!!!!!!!!!!!!
David has $520 to spend at a bicycle store for some new gear and biking outfits. Assume all prices listed include tax.
He buys a new bicycle for $303.93.
He buys 4 bicycle reflectors for $10.99 each and a pair of bike gloves for $25.25.
He plans to spend some or all of the money he has left to buy new biking outfits for $73.43 each.

Write and solve an inequality which can be used to determine xx, the number of outfits David can purchase while staying within his budget.

Answers

Answer:

x ≤ 2

Step-by-step explanation:

refer the image thank you

Answer: he can only buy 2

Step-by-step explanation: if he buys 3 it would cost 560.46

303.93 + 10.99 + 25.25 + 73.43 = 413.6

413.6 + 73.43 = 287.03

287.03 + 73.43 = 560.46

Glenda can shelve 42 boxes of cookies in 3 hours. What is her unit rate

Answers

Let’s say boxes per hour is the unit, hence 42boxes/3 hours is her rate, simplifying gives us 14boxes per hour

I NEED HELP BECAUSE UM YEA

Answers

Answer:

I believe it is B.

Help Q8-12 please please

Answers

Answer:

8-12= -4 is basic of math, try to get a calculator to help you

Step-by-step explanation:

Which expression is equivalent to 6^{-2}\times 6^{4}\normalsize?6 −2 ×6 4 ?

Answers

Answer:

dude I have no clue how to do that

Step-by-step explanation:

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