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
bearhunter [10]
3 years ago
8

Solve for x on the interval [0, 2pi] Sinx = cosx + 1

Mathematics
1 answer:
lisov135 [29]3 years ago
8 0

Answer:

π

Step-by-step explanation:

Solve for x on the interval [0, 2pi]

Given the equation

Sinx = cosx + 1

Square both sides of the equation

Sin²x = (cos x + 1)²

Sin²x = cos²x + 2cos x + 1

Since Sin²x = 1 - cos²x

1 - cos²x = cos²x + 2cos x + 1

Collect like terms

1-1-cos²x-cos²x-2cos x  = 0

-2cos²x-2cos x = 0

-2cos²x = 2cos x

-cosx = 1

cos x = -1

x = arccos -1

x = 180 degrees

<em>Hence the value of x = π</em>

You might be interested in
How do compare ratios then simplify to find the answer
gogolik [260]

"Compare ratios" covers a lot of territory. If all you want to do is find which one is larger, you can subtract or divide.

(a/b) - (c/d) > 0 . . . . means a/b is larger

(a/b) / (c/d) > 1 . . . . means a/b is larger

These operations with fractions are done using the methods of arithmetic with fractions that you have been taught.

____

"Simplify" when applied to ratios usually means common factors are removed from each of the terms.

For example, the ratio 2:12 is a ratio of even numbers, so we know both numbers have a factor of 2. (2 is a factor common to both numbers.) When we divide them both by 2, we have the reduced ratio 1:6. That is, 2:12 simplifies to become 1:6.

(It is helpful to have a good working knowledge of multiplication tables when you approach problems in simplifying ratios.)

= = = = = = = = = =

In "quick and dirty" terms, you can do the subtraction ...

\dfrac{a}{b}-\dfrac{c}{d}=\dfrac{ad-bc}{bd}

That is, you really only need to find out if (ad) > (bc) to determine if (a/b) > (c/d). A similar result is obtained when you consider division ...

\displaystyle\frac{\left(\frac{a}{b}\right)}{\left(\frac{c}{d}\right)}=\frac{a}{b}\cdot\frac{d}{c}=\frac{ad}{bc}

This will be greater than 1 if (ad) > (bc), signifying that (a/b) > (c/d).

_____

Here's an example with numbers.

... Compare 6/7 to 43/50.

... The relationship of interest will be revealed by the products 6·50 = 300 and 7·43 = 301.

... Since 300 < 301, these tell us 6/7 < 43/50.

_____

We say the above methods are "quick and dirty" because the results may need to be simplified when you're done.

For example, subtracting 1/6 from 1/2 gives

... 1/2 - 1/6 = (1·6 - 2·1)/(2·6) = 4/12

Here, numerator and denominator have a common factor of 4. Removing that gives 4/12 = 1/3.

Even if you do this by the method of common denominators, you still need to reduce the result.

... 1/2 - 1/6 = 3/6 - 1/6 = (3-1)/6 = 2/6

This must be reduced to 1/3 by removing a common factor of 2 from numerator and denominator.

3 0
3 years ago
Please someone help me with this
stiks02 [169]

Answer:give me brainlist

Step-by-step explanation:

6 0
3 years ago
Each card in a set of cards has a different number from 1 to 12 written
sergij07 [2.7K]

Answer: 35

Step-by-step explanation: i first divided 12 and 125 since there is 125 cards in total and 12 different cards which gives you 10 point something. There is 3 multiples of 4 so i multiplied 3x10 which gives you 30 and the closest answer is 35. You're welcome

4 0
3 years ago
Find the volume of the pyramid
soldier1979 [14.2K]

Answer:

264 I believe

Step-by-step explanation:

5 0
3 years ago
2. A vine called the mile-a-minute weed is known for growing at a very fast rate. It can grow up to 0.5 ft per day. How fast in
gayaneshka [121]

Answer:

.25 inches per hour

Step-by-step explanation:

.5 ft

-----------

day

We need to get to inches

1 ft = 12 inches

.5 ft          12 inches      

----------- * ------------

day             1 ft  

We also need to convert days to minutes

1 day = 24 hours

.5 ft           12 inches             1 day          

----------- * ------------   * -------------    

day             1 ft       24 hours      

6 inches

-------------

24 hours

.25 inches per hour

8 0
2 years ago
Read 2 more answers
Other questions:
  • During a flu epidemic, the number of sick people triples every week. What is the growth rate as a percent? Explain your reasonin
    12·1 answer
  • How do I find the first four terms of this geometric sequence<br><br> a1=3 and r=-3
    13·1 answer
  • The point, (-4, 1) is located in which quadrant?
    7·1 answer
  • 3s+9c=75 <br> 8s+5c=67 <br> S=? C=?
    14·1 answer
  • A plumber charges a $75 flat fee for jobs lasting up to an hour and $30 for each hour of labor after the first hour. which expre
    14·2 answers
  • Seven hundred fifteen divided by eight
    11·2 answers
  • Computisional Science
    8·1 answer
  • How many “2 x 2 x 2” cubes will fit into a “4 x 4 x 4” box?
    6·1 answer
  • You make 24 cookies using 2 cups of sugar
    14·2 answers
  • What percent is equivalent to 24/50?<br><br><br> 24%<br><br> 48%<br><br> 50%<br><br> 52%
    5·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!