How to find cos(-19pi/6)

Answers

Answer 1

Answer: Use the unit circle.

-19pi/6 is the same as 3pi + pi/6
This means that it goes around the unit circle 3pi times and ends up at 7pi/6

So -19pi/6 is equivalent to 7pi/6.

Looking at the unit circle, cos(7pi/6) = -√3/2

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Ava graphs the function h(x) = x2 + 4. Victor graphs the function g(x) = (x + 4)2. Which statements are true regarding the two graphs? Check all that apply.Ava’s graph is a vertical translation of f(x) = x2.Victor’s graph is a vertical translation of f(x) = x2.Ava’s graph moved 4 units from f(x) = x2 in a positive direction.Victor’s graph moved 4 units from f(x) = x2 in a positive direction.Ava’s graph has a y-intercept of 4.Victor’s graph has a y-intercept of 4.
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Describe a pattern in each sequence. What are the next two terms of each sequence? 2, 4, 8, 16, . . . A. add 2 to the previous term; 14, 12 B. subtract 2 from the previous term; 32, 64 C. multiply the previous term by –2; –32, 64 D. multiply the previous term by 2; 32, 64 Reset Selection

Answers

D. multiply the previous term by 2

123 grams is rounded to nearest whole. Write down the minimum possible mass it could have been.

Answers

Since we want the minimum value we are going to be rounding up from a smaller number. So we know the whole number will be 122. Now we find the smallest number that will round up which is .5. Answer is 122.5

122.4 would've rounded down.

Answer: 122.5

Step-by-step explanation: when it becomes 0.5 when rounding to the nearest whole number ot

The distributive property combines (blank) and (blank) to make multiplying whole numbers simpler

Answers

The distributive property combines addition and multiplication to make multiplying whole numbers simpler.

It combines multiplication of simpler numbers with addition.
For example:
26 x 15 can be written as: 15(10+10+6)

Answer:

Step-by-step explanation:

Mr. Prince takes his wife and two children tothe circus. If the price of a child’s ticket is 1/2
the price of an adult ticket and Mr. Prince pays
a total of $12.60, find the price of a child’s
ticket.

Answers

Facts:
MR Price takes his wife + two children
The price of adult's ticket is 2 times higher that child's
They paid $12.6 in total

Answer:
X is the price of child's ticket so equation will look:

2x (fathers' ticket) + 2x (mother's ticket) + x (first child) + x (second child) = $12.6 (total price)

6x = 12.6
X = 2.1

Child's ticket costs $2.1

Answer:

Step-by-step explanation:

10 POINTS. 1/7 written as a decimal is 0.142857 (this sequence repeats). What digit occurs in the 2012th spot after the decimal? Please explain.

Answers

1/7 = 0.142857142857142857142857142857142857142857142857142857 and so on

the pattern repeats

the first digit is 1
second digit is 4
third digit is 2
fourth digit is 8
fifth digit is 5
sixth digit is 7

and then the seventh digit is 1, and it repeats

so the six digits repeat again and again...

2012/6 = 335 2/6

It has a remainder of 2, which means that the 12th digit will be 4. because that is the second digit. After going 335 times the 6 digit patterns it will stop at the second digit which is 4.

Your answer is 4.

I hope you understood, it was kind of hard to explain :P

Can someone help me in this trig question, please? thanks A person is on the outer edge of a carousel with a radius of 20 feet that is rotating counterclockwise around a point that is centered at the origin. What is the exact value of the position of the rider after the carousel rotates 5pi/12

Answers

The exact value of the position of the rider after the carousel rotates 5π/12 is 5 (-√2 + √6), 5(√2 + √6).

The position

Since the position of the carousel is (x, y) = (20cosθ, 20sinθ) and we need to find the position when θ = 5π/12 = 5π/12 × 180 = 75°

So, substituting the value of θ into the positions, we have

(20cos75°, 20sin75°)

The value of 20cos75°

20cos75° = 20cos(45 + 30)

Using the compound angle formula

cos(A + B) = cosAcosB - sinAsinB

With A = 45 and B = 30

cos(45 + 30) = cos45cos30 - sin45sin30

= 1/√2 × √3/2 - 1/√2 × 1/2

= 1/2√2(√3 - 1)

= 1/2√2(√3 - 1) × √2/√2

= √2(√3 - 1)/4

= (√6 - √2)/4

= (-√2 + √6)/4

So, 20cos75° = 20 × (-√2 + √6)/4

= 5 (-√2 + √6)

The value of 20sin75°

20sin75° = sin(45 + 30)

Using the compound angle formula

sin(A + B) = sinAcosB + cosAsinB

With A = 45 and B = 30

sin(45 + 30) = sin45cos30 + cos45sin30

= 1/√2 × √3/2 + 1/√2 × 1/2

= 1/2√2(√3 + 1)

= 1/2√2(√3 + 1) × √2/√2

= √2(√3 + 1)/4

= (√6 + √2)/4

= (√2 + √6)/4

So, 20sin75° = 20 × (√2 + √6)/4

= 5(√2 + √6)

Thus, (20cos75°, 20sin75°) = 5 (-√2 + √6), 5(√2 + √6).

So, the exact value of the position of the rider after the carousel rotates 5π/12 is 5 (-√2 + √6), 5(√2 + √6).

Learn more about position here:

brainly.com/question/11001232

$\bf \textit{the position of the rider is clearly }20cos\left( (5\pi )/(12) \right)~~,~~20sin\left( (5\pi )/(12) \right)\n\n-------------------------------\n\n\cfrac{5}{12}\implies \cfrac{2+3}{12}\implies \cfrac{2}{12}+\cfrac{3}{12}\implies \cfrac{1}{6}+\cfrac{1}{4}\n\n\n\textit{therefore then }\qquad \cfrac{5\pi }{12}\implies \cfrac{1\pi }{6}+\cfrac{1\pi }{4}\implies \cfrac{\pi }{6}+\cfrac{\pi }{4}\n\n-------------------------------$

$\bf \textit{Sum and Difference Identities}\n\nsin(\alpha + \beta)=sin(\alpha)cos(\beta) + cos(\alpha)sin(\beta)\n\ncos(\alpha + \beta)= cos(\alpha)cos(\beta)- sin(\alpha)sin(\beta)\n\n-------------------------------\n\ncos\left( (\pi )/(6)+(\pi )/(4) \right)=cos\left( (\pi )/(6)\right)cos\left((\pi )/(4) \right)-sin\left( (\pi )/(6)\right)sin\left((\pi )/(4) \right)$

$\bf cos\left( (\pi )/(6)+(\pi )/(4) \right)=\cfrac{√(3)}{2}\cdot \cfrac{√(2)}{2}-\cfrac{1}{2}\cdot \cfrac{√(2)}{2}\implies \cfrac{√(6)}{4}-\cfrac{√(2)}{4}\implies \boxed{\cfrac{√(6)-√(2)}{4}}\n\n\nsin\left( (\pi )/(6)+(\pi )/(4) \right)=sin\left( (\pi )/(6)\right)cos\left( (\pi )/(4) \right)+cos\left( (\pi )/(6)\right)sin\left((\pi )/(4) \right)$

$\bf sin\left( (\pi )/(6)+(\pi )/(4) \right)=\cfrac{1}{2}\cdot \cfrac{√(2)}{2}+\cfrac{√(3)}{2}\cdot \cfrac{√(2)}{2}\implies \cfrac{√(2)}{4}+\cfrac{√(6)}{4}\implies \boxed{\cfrac{√(2)+√(6)}{4}}\n\n-------------------------------\n\n20\left( \cfrac{√(6)-√(2)}{4} \right)\implies 5(-√(2)+√(6))\n\n\n20\left( \cfrac{√(2)+√(6)}{4} \right)\implies 5(√(2)+√(6))$

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