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3 years ago

How do you prove #sin 5pi/12 = sin pi/6 cos pi/4 + cos pi/6 sin pi/4#?

1 answer:

6 0

You rewrite 5π/12 as 2π/12 + 3π/12 since 2 + 3 = 5.
Then you simplify the fractions into π/6 + π/4.
Then you use the sine addition identity.

sin(5π/12) = sin(π/6 + π/4) = sin π/6 cos π/4 + cos π/6 sin π/4

You might be interested in

Which fraction has a terminating decimal? - 11/19 - 4/7 - 1/3 - 3/150

babunello [35]

<h3>Answer: D) 3/150</h3>

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Explanation:

With the use of a calculator, we see that,

11/19 = 0.57894736842106...., the decimals eventually repeat; but unfortunately my calculator ran out of room to show the repeating portion
4/7 = 0.5714285714285714..., the block "571428" repeats forever
1/3 = 0.333333.... the 3s go on forever
3/150 = 0.02

So 3/150 converts to the terminating decimal 0.02

The word "terminate" means "stop". In the other decimal values, the decimal digits go on forever repeating the patterns mentioned.

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A non-calculator approach will have us simplify 3/150 into 1/50 after dividing both parts by the GCF 3. Then notice how 50 has the prime factorization of 2*5*5. The fact that the denominator 50 can be factored in terms of only 2's and 5's is enough evidence to conclude that the fraction converts to a terminating decimal.

If the denominator factors into some other primes, other than 2s and 5s, then we don't have a terminating decimal. So that's why 11/19, 4/7 and 1/3 convert to non-terminating decimals.

6 0

2 years ago

The perimeter of a rectangular garden is 37.5 feet. The width is x, and the length is 15 ft. Use the equation 2(x + 15) = 37.5 t

charle [14.2K]

Answer:

2.5

Step-by-step explanation:

37.5/15=2.5

3 0

2 years ago

Read 2 more answers

HELP ME PLEASE True or false: z=−5 is a solution to the inequality −2|z−3|<−20.

Dovator [93]

your question: 

True or false: z=−5 is a solution to the inequality −2|z−3|<−20.

answer: 

-2|z-3|<-20

-------. -----

-2 -2

|z-3|<10

equation 1: equation 2:

z-3<10. z-3>-10

z<13 z>-13

So false, z=-5 is not a solution to the inequality.

hope this helps, have a great day! :)

7 0

2 years ago

The population in the city of Millstone was approximately 2 million in 2010 and 2.2 million in 2015. What is the percent increas

Natasha_Volkova [10]

Answer:

10%

Step-by-step explanation:

Percentage increase for any change is calculated by formula

{(Final value - initial value)/initial value} * 100

Given

population in 2010 = 2 million ----------->initial value

population in 2015 = 2.2 million ----------->Final value

$Percentage \ \ increase = {(2.2 - 2)/2} *100= (0.2/2)*100 = 10%$

7 0

2 years ago

Read 2 more answers

Help me solve this..! Please!

stiv31 [10]

Answer:

x=2

Solve for x by simplifying both sides of the equation, then isolating the variable.

3 0

2 years ago