Evaluate cot 120° without using a calculator by using ratios in a reference triangle.

Answers

Answer 1

Answer: The reference angle for $120\degree$ is $60\degree$ .

Recall that $cot(120\degree) = (1)/(tan(120\degree))$

This implies that $cot(120\degree) = (1)/(tan(60\degree))$

Recall also from $30\degree - 60\degreee - 90\degree$ triangle that

$tan(60\degree)=\sqrt(3)$ and also since $120\degree$ is the in the second quadrant, the tangent ratio is negative.

Putting all together we have

$cot(120\degree) = (1)/(-\sqrt(3))$

Rationalizing the denominator gives

$cot(120\degree) = (-\sqrt(3))/(3)$

Answer 2

Answer:

Answer:

The value of cot 120° is $-(√(3))/(3)$ .

Step-by-step explanation:

Consider the trigonometric identity:

$cot(180-\theta)= -cot(\theta)$

Now use the above trigonometric identity:

$cot(120)= cot(180-60)$

$cot(180-60)= -cot(60)$

Now use the identity: $cot(\theta)=(1)/(tan(\theta))$

$-cot(60)=-(1)/(tan(60))$

Substitute the value of tan 60°.

$-(1)/(tan(60))=-(1)/(√(3))$

Now rationalize the denominator gives us:

$-(√(3))/(3)$

Hence, the value of cot 120° is $-(√(3))/(3)$ .

Related Questions

(Write an inequality to solve this problem, 13.2 Independent Practice) Pierre's parents ordered some pizzas for a party. 4.5 pizzas were eaten at the party. There were at least 5 1/2 whole pizzas left over. How many pizzas did Pierre's parents order?
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Write this in standard notation: 3.812 x 10^7
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On a coordinate grid, point N is at (−2, 4) and point S is at (6, 4). The distance (in units) between points N and S is ______. (Input only whole numbers, such as 2.)

Kofi estimated that he would run a total of 10 km in 1 h. In 1 h, he actually ran 46 times around a track 0.25 km long, going a total distance of 11.5 km.What was the percent error in Kofi’s estimate? Round to the nearest tenth of a percent, if necessary.

A.
1.5%

B.
5%

C.
13%

D.
23%

Answers

The equation to find percent error is

$(actual-theoretical)/(theoretical)*100$

where actual is the value that actually came out (in this case, 11.5 km) and theoretical is the value that was supposed to come out (in this case, 10 km). Just plug in the numbers and simplify.

$(actual-theoretical)/(theoretical)*100\n\n(11.5-10)/(10)*100=(1.5)/(10)*100=15\%\ error$

So, the true answer would be 15%. Apparently, the question you're asking takes 11.5 as the theoretical and the 10 as the actual (which I personally disagree with)

If you plugged in the numbers that way, the answer comes out to 13.04%. So, the correct answer for your answer choices is c. 13%

What is the value of 56 tens

Answers

tens = 10
56 x 10 = 560

56 tens
=56+56+56+56+56+56+56+56+56+56

= 56 x 10

=560

When the siren sounded, 440 were seen walking in the forest. If the other 360 were not seen, what fraction of the total was seen?

Answers

Fraction of the total was seen=(number of people were seen ) /(Total number of people)

Data:
number of people were seen=440
Total number of people=people saw +people didn´t see=440+360=800

Fraction of the toatal was seen=440/800=11/20

Answer: 11/20.

I got 11/9 as the answer :)

-3.75 as a mixed number in simplest form

Answers

-3.75 I think that that is 8 over 14

Can you help me if it is equivalent or not eqvalent you can help me with the rest if you want the brainless answer

Answers

10. Not equivalent.

11. Equivalent

12. Not equivalent

13. Not equivalent

14. Equivalent

15. Can't read, but I think not equivalent.

Basically, if they can be multiplied by the same scale factor they are equivalent, else they aren't.

Answer:

10. Not equivalent.

11. Equivalent

12. Not equivalent

13. Not equivalent

14. Equivalent

15. Can't read, but I think not equivalent.

Basically, if they can be multiplied by the same scale factor they are equivalent, else they aren't.

Step-by-step explanation:

what that guy said :0

3/4 (4c + 16) = 2c ÷ 9. what is c

Answers

Distribute

(3/4)(4c)+(3/4)(16)=2c/9

3c+12=2/9 c

Now subtract 2/9 c from both sides

3c+12-2/9 c=2/9 c-2/9 c

25/9 c+12 =0

Now we need to subtract 12 from both sides

25/9 c+12-12=0-12

25/9 c=-12

Just multiply both sides by 9/25 so we find the value for c

25/9 *(25/9 c)=-12(9/25)

c= -108/25

I hope that's help:0

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