Evaluate the following trigonometric expression, using the principal value for the cosine

tan(Cos-1(-1/2))

Answers

Answer 1

Given:

The expression is

[tex]\tan (\cos ^{-1}(-\dfrac{1}{2}))[/tex]

To find:

The value of given expression.

Solution:

We have,

[tex]\tan (\cos ^{-1}(-\dfrac{1}{2}))[/tex]

[tex]=\tan (\pi-\cos^{-1}(\dfrac{1}{2}))[/tex]          [tex][\because \cos^{-1}(-\theta)=\pi -\cos^{-1}\theta][/tex]

[tex]=\tan (\pi-\cos^{-1}(\cos \dfrac{\pi}{3}))[/tex]      [tex][\because \cos \dfrac{\pi}{3}=\dfrac{1}{2}][/tex]

[tex]=\tan (\pi-\dfrac{\pi}{3})[/tex]

[tex]=-\tan (\dfrac{\pi}{3})[/tex]                 [tex][\because \tan(\pi-\theta)=-\tan \theta][/tex]

[tex]=-\sqrt{3}[/tex]         [tex][\because \tan \dfrac{\pi}{3}=\sqrt{3}][/tex]

Therefore, the value of given expression is [tex]-\sqrt{3}[/tex].


Related Questions

Find the Slope of the graph

Answers

Answer:

-2/+2.5

Step-by-step explanation:

it is going down by -2 every time for y and up by 2.5 every time for x

rise over run

hope this helps

2/-2.5 or -(2/2.5) because the rise is positive 2 and the run is negative 2.5

Please help me fast ..

Answers

Plz mark it brainliest .....!

Answer these 2, i need help badly
What is 25 percent of 200?
What is 50 percent of 600?

Answers

Answer:

Step-by-step explanation:

50,300

Answer:

1. 50, 2. 300

Step-by-step explanation:

For 25 of 200, we can duplicate 100 and 25, which would turn out to be 50 and 200.

For 50 and 600, we can divide 600 by 2 to get 50 percent of it.

Answers:

25 of 200 = 50

50 of 600 = 300

Factor y^6+8z^6. Please show work!

Answers

Answer: b = 2z^2 (y^2 + 2z^2)  (y^4 - 2y z^2 + 4z^4)

Step-by-step explanation: you have to factor using the sum of the cubes formula a^3 + b^3 = (a + b) ( a^2 - ab + b^2)

Find the slope of the line that passes through (100, 56) and (28,94)

Answers

Answer:

-19/36

Step-by-step explanation:

We can find the slope using

m = ( y2-y1)/(x2-x1)

m = ( 94-56)/( 28 -100)

   = 38 / -72

   = -19/36

Please help me solve this

Answers

Answer:

1/49

Step-by-step explanation:

1/7^2 is merely 1^2/7^2  which is 1/49

Hope this helps :D plz mark brainliest if correct.

I’m literally only typing something because it said I needed 20 something characters. If you give a brainliest, give it to the dude who answered it first, I’m just confirming that he is indeed correct. Have a nice day!!

Help me (10 points )

Answers

Answer:x=10

Step-by-step explanation:x x2

Please help me. i will mark you as most brilliance and give you 5 stars! Please be specific when answering. thank you! :)

Answers

Step-by-step explanation:

5x+52=9x+20

subtract 5x on both sides

subtract 20 on both sides

32=4x

divide by 4 on both sides

x=8

plug in x to the equations for A, D, and C

A and D are 92°

C is 56°

B and C will add up to 90, so

90-56=34°

13y-6=34

add 6 on both sides

13y=40

divide by 13

y=40/13 (I don't wanna calculate that)

plz help me thanks so much ​

Answers

Answer:

0

Step-by-step explanation:

The interval -7 <= x <= 1, has endpoints:

(-7, -1) and (1, -1)

There is no rate of change (the y-coordinates are the same), hence if one draws a line to connect the two points, the line will be horizontal. Therefore, the rate of change over the interval is 0.

According to your graphing calculator, what is the approximate solution to the trigonometric inequality
cos(0.65x) > 0.45 over the interval 0

Answers

Answer:

B the answer with 1.6985

Step-by-step explanation:

did it on graphing calc

The solution of the inequality is [0, 1.699].

We will graph y=cos(0.65x)-0.45 using a calculator. Image 1.

Then we draw the boundary x=0 and x=[tex]2\pi[/tex] on the same graph. And we try to find where y>0 on that graph. Image 2.

From the graph we see that y>0 that means cos(0.65x) > 0.45 is over the interval [0, 1.699].

Learn more: https://brainly.com/question/15816805

7 times a number is the same as 1 more than 3 times the number. What is the number?

Answers

Answer:

7n=12+3n

Step-by-step explanation:

7n = 3n+1

n=1/4 or 0.25

Pretty please help me!!!
Which statement explains whether -4.5 can be a value in the shaded region


A. No it cannot, because -4.5 lies to the right of -3.5

B. No it cannot, because -4.5 lies to the right of -3.5

C. Yes it can, because-4.5 lies to the left of -3.5

D. Yes it can, because -4.5 lies to the right of -4.5​

Answers

C. Yes it can, because -4.5 lies to the left of -3.5

Given a:b and b:c, find a:b:c. Write the ratio in simplest form. a:b=10:25 and b:c=45:27

Answers

Answer:

a:b:c=2:5:3

Step-by-step explanation:

a:b=10:25

a:b=2:5(divided by 5)

b:c=45:27

b:c=5:3(divided by 9)

a:b:c=2:5:3

please hurry and help

Answers

Question 1. Volume is a measure of the amount of space that a substance or an object takes up. The basic SI unit for volume is the cubic meter (m3), but smaller volumes may be measured in cm3, and liquids may be measured in liters (L) or milliliters (mL).

Question 2. Similarities They’re both cubes, the difference is that the fish food is smaller than the other

Joyce paid $45.00 for an item at the store that was 75 percent off the original price. What was the original price?

Answers

Answer:

$60

Step-by-step explanation:

45 x 100/75 = 60

Answer:11.25

Step-by-step explanation:

45×0.75 45-33.75=11.25

Find the value of X, I need help solving this.

Answers

Answer:

32

Step-by-step explanation:

180-83=97

3*32=96

+1=97

The answer is B. 32
Because the degree of a straight line is 180°
So 83+#=180
180-83=97
3(32)+1=97

Leigh and Sara paid $1,178 last month to rent their apartment. Last month had 31 days. They divide to find out how much they paid per day. ?​

Answers

Answer:

Step-by-step explanation:

Divide 1178 by 2 will equal 589

This is how much each will pay per month

589 divided by 31 = 19 dollars a day per person

Answer: first quoitent is  31 second quotent is 6



Step-by-step explanation:

divide 1,178 with 31 so thats how you get your answer

f ( x) = 6 (1 - x ) what is the vaule of (-8)

Answers

Answer:

f(x) = 54

Step-by-step explanation:

Plugging in -8 we get f(x) = 6(1-(-8)) since there is a double negative we can simplify it to a positive --> f(x) = 6 (1 +8) now distribute 6 to all factors in ( )

6 times 1 is 6 and 6 times 8 is 48. So now we have 6 + 48 which = 54

Laurie asked 100 of her friends to choose their favorite flower. Fifteen of them chose carnations, 58 chose roses and the rest daises. What percent of her friends chose daises? 73 percent, 58 percent, 15 percent, 27 percent

Answers

Answer:

27%

Step-by-step explanation:

Mr. Sartin has 2 gallons of paint that will cover 750 Sq. Ft. He needs to cover 3000 Sq. Ft.. How many more gallons of paint does he need?

Answers

Answer:

8 galons

Step-by-step explanation:

line every information by type of units

2 gallons for 750 sq ft

? galons for 3000sq ft

crossmultiply

?*750=2*3000

divide both sides by 750

?=(2*3000) /750= 8

If F(x) =
2x-3/5
which of the following is the inverse of F(x)?

Answers

the inverse would be f^-1 (x) = 1/2x + 3/10

Write an article for publication on why students should not cheat during examination​

Answers

Answer:

The thing with exams, is that they just keep getting harder, and the consequences get more severe. Many people find themselves unable to pursue a career they want because they cannot score high on some test, and they blame the whole stupid system - but they did have 12+ years to practice taking tests.

It seems to arbitrary as a kid, but cheating tactics exist and change at all levels of education - there's not really any cumulative benefit to working on your cheating, and there's not a skill barrier to getting into cheating.

Tests on the other hand are a very arbitrary system, and the skill of taking tests can be trained. If you want to cheat, then study up on exam skills and memory tricks and studying tools. Then learn great ways to score highly on exams and it will be all the fun of cheating but you're never getting in trouble or stressed about getting caught.

In a very...amoralistic sorta way one could consider cheating to be your 'ace in the hole' sorta like steroids and athletic performance. It may be enough to push you to the next level, but if you do it early then you will never have the chance to benefit quite that much again - reputations of academic dishonesty follow you, and getting caught at the very least shows future employers that your discretion is lacking.

In that sense it is probably worthwhile to get as good at school and exams as possible, and only consider cheating when there is some life and death situation on the line and it is justifiable. Cheating is a real strategy, but it has real risks.

If you think of vegas, cheating is like trying to look at someone elses cards, or coordinate a strategy to get money out of a Casino. The casino knows you want to do this and is looking for you to do that. Now if you count cards like that recent movie about the MIT kids, there is nothing physically different about what you do - but you stack the odds in y our favor and can get on a seriously bad side of some Casinos if you are caught doing it.

Now here's the neat thing about tests - you can make way more money by being good at tests than you can by being good at counting cards (with a few notable exceptions) and you're supposed to be counting cards for the exam! The whole idea of the exam is to force you to prepare, and find some way to allow you to prove that you have mastered the material.

Exams will follow you through every stage of life, so getting good at them is an investment, and like I said it never gets easier. Like...try and fail and work new strategies all you want until your last 2 years of highschool - there's no significant consequences for failure at that point. From there forward your future really is on the line, cheat in highschool and you are at the mercy of your administrators and later the admissions officials opinion of cheaters.

With a mean of 100 and standard deviation of 15, what percentage of IQ scores are less than 110

Answers

Answer:

i think 125

Step-by-step explanation:

Asher pays $156 every 6 weeks for piano lessons. What is the price per year for piano lessons?

Answers

Answer:

About 1352$

Step-by-step explanation:

Answer:

4 3/8 cups of chopped vegetables

Step-by-step explanation:

I did 10/4 to get 2.5

Then I multiplied 2.5 x 1.75. (I did 1.75 instead of 1 3/4. They're the same)

Then I got 4.375

4.375 = 4 3/8

(3) The HCF of two numbers is 6, if one of the numbers is 42, find the other
number?​

Answers

Answer:

7jfkr

Step-by-step explanation:

its 7 because just because

There could be many possibilities for this based on the information given.

If the HCF of 42 and another number is 6, that other number can either be:

6, 12, 18, 24, 30, 36 etc... (basically any multiple of 6)

Classify the following: 9G-7

Answers

Answer:

I'm pretty sure it is a expression

find the area + perimeter of the following triangle​

Answers

Answer:

Perimeter = 14[tex]\sqrt{2}[/tex]

Area = [tex]\sqrt{42}[/tex]

Step-by-step explanation:

Find the slope of the line passing through the points (-3.6) and (8. 6).

Answers

Y=6 is the slope because no matter what the X may be, the Y will always be 6 so the line lies along the y intercept of 6

Perimeter = 2 x Length + 2 x Width
The perimeter of a rectangle is 66. If the Length is two more
than three times the Width, what is the length of that rectangle?

Answers

Answer:

25.25

Step-by-step explanation:

Let the width be x

Then the length is 3x + 2Perimeter = 66

Perimeter formula

P = 2(l +w)

Substitute values

66 = 2(3x + 2 + x)33 = 4x + 24x = 31x = 31/4x = 7.75

The length is:

3*7.75 + 2 = 25.25

You should plan on 1 1/2 pounds of turkey per person. Your family is having 10 people for Thanksgiving dinner. How many pound turkey should you plan to buy?

Answers

Answer:

Weight of total turkey need = 15 pound turkey

Step-by-step explanation:

Given:

Turkey need per person = 1[tex]\frac{1}{2}[/tex] pound turkey = 3/2 pound turkey

Total person = 10

Find:

Weight of total turkey need

Computation:

Weight of total turkey need = (3/2)(10)

Weight of total turkey need = 15 pound turkey

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