All categories

3 years ago

Determine the exact value of sin 150 degrees

Mathematics

1 answer:

avanturin [10]3 years ago

7 0

Answer:

$\frac{1}{2}$

Step-by-step explanation:

Use the identity:

$\sin(180-\theta)=\sin \theta$

We were given: $\sin 150\degree$

We can rewrite this as:

$\sin(180-30)\degree=\sin 30\degree$

On the unit circle, $\sin 30\degree=\frac{1}{2}$

This implies that:

$\sin(180-30)\degree=\sin 150\degree=\sin 30\degree=\frac{1}{2}$

Therefore the exact value of $\sin 150\degree$ is $\frac{1}{2}$

You might be interested in

A customer buy's 5 books at a bookstore for a total cost of 65$. If all the books cost the same amount, how much does 1 book cos

Gnesinka [82]

Answer: each book costs $13

Step-by-step explanation:

dividing 65 by 5 gets the answer

3 0

3 years ago

Read 2 more answers

Cammie can mow 1/2 acre in 25 minutes. If her rate is constant, Cammie says she can mow 1 1/4 acres in one hour. Is Cammie corre

Sergeu [11.5K]

Answer: No, Cammie is not correct. She can mow $1\frac{1}{5}\ acres$ in one hour (See explanation).

Step-by-step explanation:

Convert the mixed number to an impoper fraction:

1. Multiply the whole number part by the denominator of the fraction and add the product to the numerator.

2. The denominator does not change.

Then:

$1\frac{1}{4}=\frac{(1*4)+1}{4}=\frac{5}{4}$

Let be "x" the acres Cammie can mow in one hour.

You know that she can mow $\frac{1}{2}\ acre$ in 25 minutes, then you can set up the following proportion (Remember that 1 hour has 60 minutes):

$\frac{\frac{1}{2}}{25}=\frac{x}{60}$

Solving for "x", you get:

$\frac{\frac{1}{2}}{25}=\frac{x}{60}\\\\(60)(\frac{1}{50})=x\\\\x=\frac{6}{5}$

Convert from improper fraction to mixed number:

1. When you divide 6 by 5, the quotient is 1. This will be the whole number part.

2. The remainder is 1. This will be the numerator.

3. The denominator does not change.

Then:

$x=1\frac{1}{5}$

Therefore, she can mow $1\frac{1}{5}\ acres$ in one hour.

3 0

3 years ago

the distribution of heights of adult American men is approximately normal with mean 68 in and a standard deviation of 2.5 in wha

melamori03 [73]

Let x be a random variable representing the heights of adult American men. Since it is normally distributed and the population mean and standard deviation are known, we would apply the formula,

z = (x - mean)/Standard deviation

From the information given,

mean = 68

standard deviation = 2.5

The probability that the height of a selected adult is between 63 and 73 is expressed as

$P(68\leq x\leq73)$

For x = 63,

z = (63 - 68)/2.5 = -2

Looking at the normal distribution table, the probability corresponding to the z score is 0.02275

For x = 73,

z = (73 - 68)/2.5 = 2

Looking at the normal distribution table, the probability corresponding to the z score is 0.97725

Therefore,

$P(68\text{ }\leq x\leq73)\text{ = 0.97725 - 0.0}2275\text{ = 0}.9545$

Thus, the percentage of men are between 63 and 73 is

0.9545 * 100 = 95.45%

Rounding up to the nearest percentage, the answer is 95%

8 0

1 year ago

Fifty-four is ___% of 60.<br><br> 20 points offered

prisoha [69]

Answer:

54÷60×100= 90%

Step-by-step explanation:

90%

cmon man

4 0

3 years ago

Read 2 more answers

A realtor sold a home for $341,100 The commission was 4% of the sale price; however, the realtor receives only 60% of the com

Pepsi [2]

Answer:

The relator recived $8,186.4

Step-by-step explanation:

What you have to do is find the 60% of the commission. Commission is 4% of $341,100 (100%)

First do a cross multiplication to find 4% of $341,100

100% ___ $341,100

4%______x:

$x=(4*341,100)/100=13,644$

So, the 4% of $341,100 is $13,466

Now you have to find the 60% of $13,466

100% ___ $13,466

60%______x:

$x=(60*13,466)/100=8,186.4$

The answer is: $8,186.4

3 0

3 years ago