1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
kobusy [5.1K]
3 years ago
10

If sin theta= 2/3 and tan theta<0, what is the value of cos theta

Mathematics
2 answers:
Sergeeva-Olga [200]3 years ago
8 0
Cos
θ
=
√
5
3

or it could be cos
θ
=
√
5
−
3

Explanation:
Since sin
θ
is negative, it can be in the third or fourth quadrant
Drawing your right-angled triangle, place your
θ
in one of three corners. Your longest side will be 3 and the side opposite the
θ
will be -2. Finally, using Pythagoras theorem, your last side should be
√
5

Now, if your triangle was in the third quadrant, you would have
cos
θ
=
√
5
−
3
since cosine is negative in the third quadrant
But if your triangle was in the fourth quadrant, you would have
cos
θ
=
√
5
3
since cosine is positive in the fourth quadrant
PilotLPTM [1.2K]3 years ago
6 0

Answer: - sqrt 5 / 3

Step-by-step explanation:

You might be interested in
-3(t+5)+(4t+2)=8
Tanya [424]
First use distributive property on -3(t+5), which would be -3t minus -15.

Then, add all like terms: -3t-15+4t+2 ---> -3t+4t+2-15 --> t-13.

t-13=8, add 13 to both sides. This cancels the -13 and makes 8 to 21.

Therefore, t=21
7 0
3 years ago
Read 2 more answers
How many subsets of at least one element does a set of seven elements have?
Tomtit [17]

\boxed{\large{\bold{\blue{ANSWER~:) }}}}

For each subset it can either contain or not contain an element. For each element, there are 2 possibilities. Multiplying these together we get 27 or 128 subsets. For generalisation the total number of subsets of a set containing n elements is 2 to the power n.

3 0
3 years ago
Loretta’s income last year was $81,300. She made $56,800 at her salaried job and had additional passive income. If Loretta earne
NARA [144]
81300 - 56800 = 24500 passive income for the year.
24500/12 = 2041.67 passive income per month
8 0
3 years ago
Read 2 more answers
Find the equation of the sphere if one of its diameters has endpoints (4, 2, -9) and (6, 6, -3) which has been normalized so tha
Pavel [41]

Answer:

(x - 5)^2 + (y - 4)^2 + (z - 6)^2 = 14.

(Expand to obtain an equivalent expression for the sphere: x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0)

Step-by-step explanation:

Apply the Pythagorean Theorem to find the distance between these two endpoints:

\begin{aligned}&\text{Distance}\cr &= \sqrt{\left(x_2 - x_1\right)^2 + \left(y_2 - y_1\right)^2 + \left(z_2 - z_1\right)^2} \cr &= \sqrt{(6 - 4)^2 + (6 - 2)^2 + ((-3) - (-9))^2 \cr &= \sqrt{56}}\end{aligned}.

Since the two endpoints form a diameter of the sphere, the distance between them would be equal to the diameter of the sphere. The radius of a sphere is one-half of its diameter. In this case, that would be equal to:

\begin{aligned} r &= \frac{1}{2} \, \sqrt{56} \cr &= \sqrt{\left(\frac{1}{2}\right)^2 \times 56} \cr &= \sqrt{\frac{1}{4} \times 56} \cr &= \sqrt{14} \end{aligned}.

In a sphere, the midpoint of every diameter would be the center of the sphere. Each component of the midpoint of a segment (such as the diameter in this question) is equal to the arithmetic mean of that component of the two endpoints. In other words, the midpoint of a segment between \left(x_1, \, y_1, \, z_1\right) and \left(x_2, \, y_2, \, z_2\right) would be:

\displaystyle \left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right).

In this case, the midpoint of the diameter, which is the same as the center of the sphere, would be at:

\begin{aligned}&\left(\frac{x_1 + x_2}{2},\, \frac{y_1 + y_2}{2}, \, \frac{z_1 + z_2}{2}\right) \cr &= \left(\frac{4 + 6}{2},\, \frac{2 + 6}{2}, \, \frac{(-9) + (-3)}{2}\right) \cr &= (5,\, 4\, -6)\end{aligned}.

The equation for a sphere of radius r and center \left(x_0,\, y_0,\, z_0\right) would be:

\left(x - x_0\right)^2 + \left(y - y_0\right)^2 + \left(z - z_0\right)^2 = r^2.

In this case, the equation would be:

\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z - (-6)\right)^2 = \left(\sqrt{56}\right)^2.

Simplify to obtain:

\left(x - 5\right)^2 + \left(y - 4\right)^2 + \left(z + 6\right)^2 = 56.

Expand the squares and simplify to obtain:

x^2 - 10\,x + y^2 - 8\, y + z^2 - 12\, z + 63 = 0.

8 0
3 years ago
Points F,G, and H are collinear such that FG:FH=2/3.If a directed line segment begins at F(-3,2) and ends at H (-3,7), find the
Nana76 [90]
We consider the x- and y-coordinates separately. Let the coordinates of G be (x, y). Now considering the x-coordinates:
FG/FH = (x - (-3)) / (-3 - (-3)) = 2/3
x + 3 = (2/3)(6)
x = 1
For the y-coordinates:
FG/FH = (y - 2) / (7 - 2) = 2/3
y - 2 = (2/3)(5)
y = 16/3
Therefore the coordinates of G are (1, 16/3).
8 0
3 years ago
Other questions:
  • I do not get this
    7·1 answer
  • An angle measures 12 degrees less than three times its supplement. Find the measure of the angle.
    13·1 answer
  • If m 5=102, then m 8=
    10·1 answer
  • WILL MARK THE BRAINIEST!!! LOTS OF POINTS!! HELP NOW
    8·1 answer
  • How do you fit numbers into a faction?
    9·1 answer
  • Write the expression: 4 divided by the sum of x and 7. A) 4 + 7 x B) x 4 + 7 C) x + 7 4 D) 4 x + 7
    14·1 answer
  • Can we conclude that x - 4 is a factor of the polynomial 4x^3-20x^2+18x-12?<br> How do you know?
    7·1 answer
  • The population of the city of Woodville is growing at a constant rate. The expression 38,000 + 2,400x models Woodville's populat
    8·1 answer
  • Ryan plays football Monday through Friday for 3 hours each night how many hours does he play in a 3 week period
    11·1 answer
  • Solve for x <br> answer must be simplified <br> -30&lt; x/-4
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!