Helpppppppppppppp!!!!!!!!!!!!!!!

HELP! Find the value of sin 0 if tan 0 = 4; 180 < 0< 270

BabaBlast [244]

Hi there! Use the following identities below to help with your problem.

$\large \boxed{sin \theta = tan \theta cos \theta} \\ \large \boxed{tan^{2} \theta + 1 = {sec}^{2} \theta}$

What we know is our tangent value. We are going to use the tan²θ+1 = sec²θ to find the value of cosθ. Substitute tanθ = 4 in the second identity.

$\large{ {4}^{2} + 1 = {sec}^{2} \theta } \\ \large{16 + 1 = {sec}^{2} \theta } \\ \large{ {sec}^{2} \theta = 17}$

As we know, sec²θ = 1/cos²θ.

$\large \boxed{sec \theta = \frac{1}{cos \theta} } \\ \large \boxed{ {sec}^{2} \theta = \frac{1}{ {cos}^{2} \theta} }$

And thus,

$\large{ {cos}^{2} \theta = \frac{1}{17}} \\ \large{cos \theta = \frac{ \sqrt{1} }{ \sqrt{17} } } \\ \large{cos \theta = \frac{1}{ \sqrt{17} } \longrightarrow \frac{ \sqrt{17} }{17} }$

Since the given domain is 180° < θ < 360°. Thus, the cosθ < 0.

$\large{cos \theta = \cancel\frac{ \sqrt{17} }{17} \longrightarrow cos \theta = - \frac{ \sqrt{17} }{17}}$

Then use the Identity of sinθ = tanθcosθ to find the sinθ.

$\large{sin \theta = 4 \times ( - \frac{ \sqrt{17} }{17}) } \\ \large{sin \theta = - \frac{4 \sqrt{17} }{17} }$

Answer

sinθ = -4sqrt(17)/17 or A choice.

4 0

3 years ago

The mean of a normal probability distribution is 500 and the standard deviation is 10. about 95 percent of the observations lie

PIT_PIT [208]

Answer:

So about 95 percent of the observations lie between 480 and 520.

Step-by-step explanation:

The Empirical Rule states that, for a normally distributed random variable:

68% of the measures are within 1 standard deviation of the mean.

95% of the measures are within 2 standard deviations of the mean.

99.7% of the measures are within 3 standard deviations of the mean.

In this problem, we have that:

The mean is 500 and the standard deviation is 10.

About 95 percent of the observations lie between what two values?

From the Empirical Rule, this is from 500 - 2*10 = 480 to 500 + 2*10 = 520.

So about 95 percent of the observations lie between 480 and 520.

5 0

3 years ago

At a collage bookstore Clara purchased a math textbook and a novel that cost a total of $54 not including tax if the price of th

diamong [38]

Answer:

m+n=54 and m=3n+8 is the system of equations that could be used to determine the price of each book.

Step-by-step explanation:

Given,

Total cost of maths book and novel = $54

Let,

Cost of maths book = m

Cost of novel = n

According to given statement;

m+n=54 Eqn 1

the price of the math textbook, m, is $8 more than 3 times the price of the novel

m = 3n+8 Eqn 2

m+n=54 and m=3n+8 is the system of equations that could be used to determine the price of each book.

Step-by-step explanation:

3 0

3 years ago

Represent the relationship between the total cost and the number of items, if total cost t is proportional to the number n of it

kvv77 [185]

Answer:

t = pn

Step-by-step explanation:

We are to find the relationship between total cost and the number of items.

First we would represent the relationship between total cost and number of items with variables

Let the total cost = t

and the number of items = n

Total cost t is proportional to the number n of items:

t ∝ n

t = kn

where k is constant

Since it is purchased at a constant price p, the constant of proportionality would be p. the k would be replaced with p

t = pn

5 0

3 years ago

Draw a coordinate plane.

natulia [17]

The coordinate of points K, L and M is the location of the points on a coordinate plane

<h3>How to determine the missing coordinates?</h3>

The given parameters are:

K = (10, )

L = ( ,10)

M = (30, )

The question has missing parameters.

So, I will assume that the line is a perfectly horizontal line.

This means that the y-coordinates of points K, L and M are equal.

The y-coordinate of point L is 10.

So, we have:

K = (10, 10)

L = ( ,10)

M = (30, 10)

Assume that point L is halfway points K and M, then we have:

K = (10, 10)

L = (20, 10)

M = (30, 10)

See attachment for the diagram of the coordinate plane showing the line

Read more about coordinate planes at:

brainly.com/question/7243416

#SPJ1

8 0

2 years ago