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
Olin [163]
3 years ago
11

If (cos)x= 1/2 what is sin(x) and tan(x)? Explain your steps in complete sentences.

Mathematics
2 answers:
Natasha_Volkova [10]3 years ago
6 0
The correct answers are:
1) sin(x) = \frac{ \sqrt{3} }{2}
2) tan(x) = \sqrt{3}

Explanation:
Given:
cos(x) =  \frac{1}{2}

Step 1:
Since, according to the Trigonometric identity:
sin^2(x) + cos^2(x) = 1 -- (1)

Step 2:
Plug in the value of cos(x) in equation (1):
sin^2(x) + ( \frac{1}{2} )^2 = 1 \\ sin^2(x) + \frac{1}{4} = 1 \\ sin^2(x)  =  \frac{3}{4}

Step 3:
Take square-root on both sides:
\sqrt{sin^2(x)} =  \sqrt{\frac{3}{4}}

sin(x) = \frac{ \sqrt{3} }{2}

Now to find the tan(x), we would use the following formula:

tan(x) = \frac{sin(x)}{cos(x)} --- (2)

Plug in the values of sin(x) and cos(x) in equation (2):
tan(x) = \frac{ \frac{ \sqrt{3} }{2} }{ \frac{1}{2} }

Hence tan(x) = \sqrt{3}
Wewaii [24]3 years ago
3 0

Answer:

The value of \sin x=\frac{\sqrt{3}}{2}

The value of \tan x=\sqrt{3}

Step-by-step explanation:

Given = \cos x=\frac{1}{2}

To find :\sin x=? and \tan x=?

Solution:

We know that, if the cosine function of an angle is\frac{1}{2} then the angle is equal to the 60°.

\cos x=\frac{1}{2}

x = 60°

The value of the :

\sin x=\sin 60^o=\frac{\sqrt{3}}{2}

We know that ratio of sine function to the cosine function is equal tto the tangent

\tan x=\frac{\sin x}{\cos x}=\frac{\frac{\sqrt{3}}{2}}{\frac{1}{2}}=\sqrt{3}

The value of \sin x=\frac{\sqrt{3}}{2}

The value of \tan x=\sqrt{3}

You might be interested in
10×3 tens in standard form
tamaranim1 [39]

The answer to that would be 30

5 0
3 years ago
Read 2 more answers
Y=? cm<br> A15<br> B.10<br> C.3<br> D.5
Gelneren [198K]
What is the question?
3 0
3 years ago
Read 2 more answers
Which equation represents the line of reflection for this graph?
tino4ka555 [31]

Answer:

x= 0

Step-by-step explanation:

Because it scale factor

7 1
3 years ago
Consider the population of all 1-gallon cans of dusty rose paint manufactured by a particular paint company. Suppose that a norm
Artemon [7]

Answer:

a) 0.5.

b) 0.8413

c) 0.8413

d) 0.6826

e) 0.9332

f) 1

Step-by-step explanation:

Problems of normally distributed samples are solved using the z-score formula.

In a set with mean \mu and standard deviation \sigma, the zscore of a measure X is given by:

Z = \frac{X - \mu}{\sigma}

The Z-score measures how many standard deviations the measure is from the mean. After finding the Z-score, we look at the z-score table and find the p-value associated with this z-score. This p-value is the probability that the value of the measure is smaller than X, that is, the percentile of X. Subtracting 1 by the pvalue, we get the probability that the value of the measure is greater than X.

In this problem, we have that:

\mu = 6, \sigma = 0.2

(a) P(x > 6) =

This is 1 subtracted by the pvalue of Z when X = 6. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{6-6}{0.2}

Z = 0

Z = 0 has a pvalue of 0.5.

1 - 0.5 = 0.5.

(b) P(x < 6.2)=

This is the pvalue of Z when X = 6.2. So

Z = \frac{X - \mu}{\sigma}

Z = \frac{6.2-6}{0.2}

Z = 1

Z = 1 has a pvalue of 0.8413

(c) P(x ≤ 6.2) =

In the normal distribution, the probability of an exact value, for example, P(X = 6.2), is always zero, which means that P(x ≤ 6.2) = P(x < 6.2) = 0.8413.

(d) P(5.8 < x < 6.2) =

This is the pvalue of Z when X = 6.2 subtracted by the pvalue of Z when X  5.8.

X = 6.2

Z = \frac{X - \mu}{\sigma}

Z = \frac{6.2-6}{0.2}

Z = 1

Z = 1 has a pvalue of 0.8413

X = 5.8

Z = \frac{X - \mu}{\sigma}

Z = \frac{5.8-6}{0.2}

Z = -1

Z = -1 has a pvalue of 0.1587

0.8413 - 0.1587 = 0.6826

(e) P(x > 5.7) =

This is 1 subtracted by the pvalue of Z when X = 5.7.

Z = \frac{X - \mu}{\sigma}

Z = \frac{5.8-6}{0.2}

Z = -1.5

Z = -1.5 has a pvalue of 0.0668

1 - 0.0668 = 0.9332

(f) P(x > 5) =

This is 1 subtracted by the pvalue of Z when X = 5.

Z = \frac{X - \mu}{\sigma}

Z = \frac{5-6}{0.2}

Z = -5

Z = -5 has a pvalue of 0.

1 - 0 = 1

5 0
3 years ago
Which problem can we solve with 27 : 3?
N76 [4]

Answer:

La Tasha has 27 rabbit stickers. She splits the stickers

evenly among 3 pieces of paper. How many stickers

did La Tasha put on each piece of paper?​

Step-by-step explanation:

6 0
3 years ago
Other questions:
  • Eric has 34 toy cars . He gives 4 cars to his little brother . Then Eric puts an equal number of his you cars in 5 bags . How ma
    12·2 answers
  • Please help me!!
    5·1 answer
  • If the sum of the interior angles of a polygon is 540, then how many sides does the polygon have?
    7·1 answer
  • ¿Cuántas soluciones tiene la ecuación 2 + 6 (x - 4) = 3x - 18 + 3x?
    9·1 answer
  • Vinyl wallpaper is needed to cover 4 walls of a room each wall measures 12 feet By 8 feet and each bolt of wallpaper covers 72 s
    7·1 answer
  • Edward’s recipe for salad uses a ratio of 3 3/4 cups of lettuce to 1/2 lb of tomatoes. Use a complex fraction to compare the amo
    10·1 answer
  • HELP I NEED HELP PLZ
    10·1 answer
  • I need help with this
    11·1 answer
  • Geometry question pls help
    8·1 answer
  • What is the y-intercept of a line that has a Slope of 3 and passes through point (-1, -7)
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!