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3 years ago

Given that sin θ = 0.5, where π/2 < θ < π , find cos θ .

Mathematics

1 answer:

kow [346]3 years ago

4 0

Answer:

cos theta is -0.866

Step-by-step explanation:

We have the range as between 90 and 180 degrees (pi is the same as 180 degrees)

The quadrant we are considering here is the 2nd quadrant

Mathematically;

if sin theta = 0.5

theta = arc•sin 0.5

theta = 30 degrees

The angle on the second quadrant is of the likes;

180-theta

so we have 180-30

and that is 150 degrees

cos (150) is thus; -0.866

You might be interested in

Find the derivative of f(x) = 4 divided by x at x = 2.

polet [3.4K]

<h2>Hello!</h2>

The answer is:

$f'(2)=-1$

To solve this problem, first we need to derivate the given function, and then, evaluate the derivated function with x equal to 2.

The given function is:

$f(x)=\frac{4}{x}$

It's a quotient, so, we need to use the following formula to derivate it:

$f'(x)=\frac{d}{dx}(\frac{u}{v}) =\frac{v*u'-u*v'}{v^{2} }$

Then, of the given function we have that:

$u=4\\v=x$

So, derivating we have:

$f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{x*(4)'-4*(x)'}{x^{2} }$

$f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{x*0-4*1}{x^{2} }$

$f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{0-4}{x^{2} }$

$f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{-4}{x^{2} }$

Hence,

$f'(x)=\frac{d}{dx}(\frac{4}{x}) =\frac{-4}{x^{2} }$

Now, evaluating with x equal to 2, we have:

$f'(2)=\frac{-4}{(2)^{2} }$

$f'(2)=\frac{-4}{4}$

$f'(2)=-1$

Therefore, the answer is:

$f'(2)=-1$

Have a nice day!

4 0

3 years ago

Read 2 more answers

A rock is thrown from the top of a tall building.The distance in feet between the rock and the ground t seconds after thrown is

marusya05 [52]

Answer:

0.448 seconds

Step-by-step explanation:

d = -16t² -4t + 412

find t when d = 407

substituting d = 407 into the equation:

407 = -16t² -4t + 412 (subtract 407 from both sides)

-16t² -4t + 412 - 407 = 0

-16t² -4t + 5 = 0 (multiply both sides by -1)

16t² + 4t - 5 = 0

solving using your method of choice (i.e completing the square or using the quadratic equation), you will end up with

t = (-1/8) (1 + √21)= -0.70 seconds (not possible because time cannot be negative)

t = (-1/8) (1 -√21) = 0.448 seconds (answer)

4 0

3 years ago

Of the $2400 Mr Calvin earned, he spent 3/8 on food, 1/3 on taxes and 1/6 on other expenses. Find out how much all this is in do

sattari [20]

Answer: $300

Step-by-step explanation:

Mr. Calvin earned $\$2400$

He spent $\frac{3}{8}$ on food i.e.

$\Rightarrow \dfrac{3}{8}\times 2400=\$900$

$\dfrac{1}{3}\quad \text{on taxes i.e.}\\\\\Rightarrow \dfrac{1}{3}\times 2400=\$800$

$\dfrac{1}{6}\ \text{on other expenses i.e.}\\\\\Rightarrow \dfrac{1}{6}\times 2400=\$400$

Remaining money = $2400-900-800-400=\$300$

So, he saved $300 after expenses

7 0

3 years ago

Major league baseball salaries averaged $1.5 million with a standard deviation of $0.8 million in 1994. suppose a sample of 100

seropon [69]

Answer: The probability that the avg. salary of the 100 players exceeded $1 million is approximately 1.

Explanation:

Step 1: Estimate the standard error. Standard error can be calcualted by dividing the standard deviation by the square root of the sample size:

$SE=\frac{0.8}{\sqrt{100}}=\frac{0.8}{10} = 0.08$

So, Standard Error is 0.08 million or $80,000.

Step 2: Next, estimate the mean is how many standard errors below the population mean $1 million.

$\frac{1 - 1.5}{0.08}$

$=-6.250$

-6.250 means that $1 million is siz standard errors away from the mean. Since, the value is too far from the bell-shaped normal distribution curve that nearly 100% of the values are greater than it.

Therefore, we can say that because 100% values are greater than it, probability that the avg. salary of the 100 players exceeded $1 million is approximately 1.

5 0

3 years ago

Stan's, marks, and wayne's ages are consecutive whole numbers. stan is the youngest, and wayne is the oldest. the sum of their a

White raven [17]

Stan's, Mark's and Wayne's ages are 35 , 36 and 37 years respectively.

<em><u>Explanation</u></em>

Stan's, Mark's and Wayne's ages are <u>consecutive whole numbers</u> and Stan is the youngest and Wayne is the oldest.

So, lets assume that Stan's, Mark's and Wayne's ages are $n, n+1$ and $n+2$