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3 years ago

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Please help, geometry homework. Answer true or false for the following statements. The ones that are marked “ T” or “ F “ are al

ready done, if I am wrong, please let me know.

1 answer:

neonofarm [45]3 years ago

5 0

1. False
2. True
3. False
4. False
5. False

13. False
14. False

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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

Please help me on this question.

EastWind [94]

Answer:

2nd choice i think tell me if its right

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3 years ago

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Smallest to largest 0.8 30% 3/5

rjkz [21]

Change everything to the same thing. See like how 30% is a percent you can move the decimal of 0.8 to make it a percent like 80%, then for 3/5 you divide 3 by 5 and you get 0.6 then you can move the decimal to get 60%. So all you have to do now is order the percentages from smallest to largest. Like so 30%, 60%, 80% which then ends up as 30%, 3/5, 0.8.

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3 years ago

What is the solution to the equation below log7 ANSWER FAST PLEASE

Soloha48 [4]

Log7+log(x-4)=1
Subtract log 7 from both sides
Log(x-4)=1-log7
As 1-log7 = log (10/7)
Log(x-4)=log (10/7)
As bases of logs are same.
we get
x-4=10/7
Add 4 to both sides
x=10/7 + 4
simplify
x=38/7

Answer: x=38/7

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3 years ago

Grape juice comes in a 64 oz bottle. Apple juice comes in a 80 ounce bottle. Both juices will be poured into cups of equal size

nika2105 [10]

An 80 ounce cup i may be wrong

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3 years ago