Ayone amos right now gonna be answering : yungbreezyf2

Given that sec (x) = 2 and cosec (x) is negative,

weeeeeb [17]

Answer:

i) sin(2x) = $-\frac{\sqrt{3}}{2}$

ii) cot(x+360) = $-\frac{\sqrt{3}}{3}$

iii) sin(x-180) = $\frac{\sqrt{3}}{2}$

Step-by-step explanation:

sec(x) = 2

Since cos(x) is reciprocal of sec(x), this means:

cos(x) = $\frac{1}{2}$

cosec(x) is negative , this means sin(x) is also negative. The only quadrant where cos(x), sec(x) are positive and sin(x), cosec(x) are negative is the 4th quadrant. Hence the terminal arm of the angle x is in 4th quadrant.

Part i)

sin(2x) can be simplified as:

sin(2x) = 2 sin(x) cos(x)

First we need to find the value of sin(x). According to Pythagorean identity:

$sin^{2}(x)=1-cos^{2}(x)\\\\ sin(x)=\pm \sqrt{1-cos^{2}(x)}$

Since, angle is in 4th quadrant, sin(x) will be negative. So considering the negative value of sin(x) and substituting the value of cos(x), we get:

$sin(x)=- \sqrt{1-cos^{2}(x)}\\\\ sin(x)=-\sqrt{1-(\frac{1}{2})^{2}}\\\\ sin(x)=-\frac{\sqrt{3}}{2}$

So,

$sin(2x)=2 \times -\frac{\sqrt{3} }{2} \times \frac{1}{2}\\\\ sin(2x)=-\frac{\sqrt{3}}{2}$

Part ii)

We have to find cot(x + 360)

An addition of 360 degrees to the angle brings it back to the same terminal point. So the trigonometric ratios of the original angle and new angle after adding 360 or any multiple of 360 stay the same. i.e.

cot(x + 360) = cot(x)

$cot(x) = \frac{cos(x)}{sin(x)}\\$

Using the values, we get:

$cot(x)=\frac{\frac{1}{2}}{-\frac{\sqrt{3}}{2} }\\\\ cot(x)=-\frac{\sqrt{3}}{3}$

Part iii)

We need to find the value of sin(x - 180)

sin(x - 180) = - sin(x)

Addition or subtraction of 180 degrees changes the angle by 2 quadrants. The sign of sin(x) becomes opposite if the angle jumps by 2 quadrants. For example, sin(x) is positive in 1st quadrant and negative in 3rd quadrant.

So,

sin(x - 180) = $-(-\frac{\sqrt{3}}{2}) = \frac{\sqrt{3}}{2}$

6 0

3 years ago

The city's budget is 8,000,000. the city actually spends 12,000,000 what is the city's deficit

kvv77 [185]

Answer: 4,000,000

Step-by-step explanation: This is the amount that exceeds of what they actually should be spending or using I guess.

6 0

2 years ago

HCF and LCM questions

mina [271]

<h3>HCF and LCM Questions</h3>

Responses:

6. (i) 27

(ii) 4 rose stalks, 3 lily stalks, and 2 orchid stalks

7. After 18 minutes

8. (i) May 7th

(ii) Every 12 days

<h3>How can the HCF and LCM be used to find the right responses?</h3>

6. The number of stalks of roses = 108

Number of stalks of lilies = 81

Number of stalks of orchids = 54

(i) The largest number of baskets that can be packed is given by the

Highest Common Factor, GCF , or HCF, of 108, 81, and 54, which is

found as follows;

54 = 2 × 27

81 = 3 × 27

108 = 4 × 27

Therefore;

The HCF of 108, 81, and 54 is 27

Which gives;

The largest number of baskets that can be packed = <u>27</u>

(ii) From the above factors, we have;

Number of rose stalks per basket = <u>4</u>

Number of lilies per basket =<u> 3</u>

Number of orchids per basket =<u> 2</u>

7. Length of the circular path = 1 km. = 1,000 m.

Time Lixin takes to walk one round = 18 minutes = 1,080 seconds

Time Khairul takes to run one round = 360 seconds

Time Devi takes to cycle 2 rounds = 4 minutes

Therefore;

Time Devi takes to complete 1 round = $\frac{4}{2}$ = 2 minutes = 120 seconds

Required:

The time at which the three of them will next meet at the starting point

Solution:

The time at which they meet at the starting point is given as the lowest

common multiple, LCM of 1,080, 360, and 120, which is given as

follows.

1,080 = 360 × 3

1,080 = 120 × 9

1,080 = 1,080 × 1

Therefore;

The LCM of 1,080, 360, and 120 is 1,080

The time they will next meet at the starting point is after 1,080 seconds which is <u>18 minutes</u>

8. The days off of Nora = Every 4 days

Days off for Amirah = Every 6 days

Nora's last day of = 29 April

Amirah's last day off = 1 May

(i) The next time they will both have the same day off is given as follows;

6·x = 2 + 4·x

2·x = 2

x = 1

Therefore, the next time Amirah has a day off, which is 1 May + 6 days = 7 May, they will both have the same day off.

They will both have the same day off on May 7

(ii) The number of days that it will take for them to have the same day off is given by the HCF of 4 and 6, which is <u>every 12 days</u>.

Learn more about LCM and HCF here:

brainly.com/question/20293084

brainly.com/question/14387448

7 0

2 years ago

Latitude measures the distance ( in degrees-north or south ) above the equator. The equator has a latitude of 0° . Your friend l

IrinaK [193]

The friend lives in a town that is 10° farther north than 40° N. The latitude of that town is 40° +10° = 50° N. When that latitude is reflected across the equator, N changes to S. The new latitude would be c. 50° S.

7 0

2 years ago

Eight less than three times a number is -14

Ahat [919]

Answer: -2

Step-by-step explanation:

Let the number be x

3x - 8= -14

3x= -14+8

3x= -6

x= -2

5 0

2 years ago