Given the quadrant of theta in standard position and a trigonometric function value of theta , find the exact value for the indicated function. I, cos theta = 0.25; tan theta

Answer:

[tex]\sqrt{15}[/tex]

Step-by-step explanation:

[tex]\cos(\theta)=\frac{1}{4}[/tex] is given.

My attempt will to be to use the Pythagorean Identity:

[tex]\cos^2(\theta)+\sin^2(\theta)=1[/tex]

[tex](\frac{1}{4})^2+\sin^2(\theta)=1[/tex]

[tex]\frac{1}{16}+\sin^2(\theta)=1[/tex]

Subtract 1/16 on both sides:

[tex]\sin^2(\theta)=\frac{15}{16}[/tex]

We have the following quotient identity:

[tex]\frac{\sin^2(\theta)}{\cos^2(\theta)}=\tan^2(\theta)[/tex]

[tex]\frac{\sin^2(\theta)}{\cos^2(\theta)}=\frac{\frac{15}{16}}{\frac{1}{16}}[/tex]

Multiply the numerator and denominator by 16. This is multiplying the fraction by 1 so this doesn't change the value of the fraction.

[tex]\tan^2(\theta)=\frac{15}{1}[/tex]

[tex]\tan^2(\theta)=15[/tex]

Square root both sides:

[tex]\tan(\theta)=\pm \sqrt{15}[/tex]

Since we are in the first quadrant then all 6 trigonometric functions are positive there so the answer is [tex]\sqrt{15}[/tex].

how to write this numbers in word 23.6​

HELP PLZ!!!! I BEG YOU PLZ!!!!! HURRY!!! FACTS!!! I'll GIVE BRAINLYEST!!!! 10 POINTS!!!!

Which transformation were used to create triangle J'K'L?

(There is no picture that comes with it!!!)

A. dilation by a scale factor of 2 and a rotation of 90(degrees) clockwise about the origin.
B. dilation by a scale factor of 1/2 and a reflection across the x-axis
C. dilation by a scale factor of 2 and a rotation of 90(degrees) counter-clockwise about the origin
D. dilation by a scale factor of 1/2 and a reflection across the y-axis

Please help me with this

Can someone help me with this question? I need the statement reasoning! Thank you so much I will mark brainliest!

To the man and women who adopted a helpless child when she was brought to them;
To the teachers who never really cared and ignored my problems;To those who never cared, never spoke, probably never knew my name;To the one true friend, whose caring was the only thing that prevented this even from happening sooner; Do not weep for me, or mourn my passing. I say this not because I expect to be missed, but to allow those who truly did not care go on with their lives with a clean conscience and dry eyes. I know you don’t want to weep for me. So don’t. But I do ask you to listen to the final words of a young girl who has taken charge of her own destiny.Perhaps my parents might feel something inside which causes them to shed tears. They may pretend that it’s sorrow for their “loss”, but I hope it is something else. Perhaps sorrow for bringing a child into this world when they really didn’t have the time or desire to raise her. I wasn’t the product of love, born of a desire to prepare another human being to grow and lead the human race. I was merely the next acquisition, the next task, the next project on their list of things that bring significance.No child should be brought into this world for the mere purpose of being just another possession. Why can’t you accept the things that make other people different rather than insisting everyone conforms to your will?Sure, some did offer friendly gestures. Drew Wilson often would greet me and ask about my life. Not that I ever felt comfortable enough to tell her anything; I never trusted her enough to give her the chance. What was the purpose? You left me isolated and alone, and no words I could say can convey to you the suffering you caused. I could name names, but in doing so, I would do more now for you than you ever did for me in life.I do not know if what awaits me when I get down off this rope. Will there be a void? Or will I come face to face with God? I just don’t care anymore. If you’re anything like your people, I wouldn’t want to know you. You preached to love one another, yet I’ve felt everything except love from Christians. Even if I could know you were different, well, I still reject you. You have left your “followers” to treat people like me poorly. You have allowed so many of the people you “love”, including me, to suffer. So you want me to trust you with my life? I don’t want to spend eternity with a careless deity like you, or with the company you keep.As my final moments tick away, I wonder what impact these words will create. It depends first on this web site being found, as I doubt whether school administration will want such venom spoken publicly about their lack of caring. Still, the Internet is a remarkable place where even the least significant individual can be heard. Will anyone listen? Will anyone take action? Will students pause and pay attention to the hur*ing hearts around them? And even if they do, will it be a temporary salve for their egos, to convince themselves they’re really not bad people or will real change happen?My heart certainly goes out to my fellow outsiders. With me gone, some of you will certainly feel more of the pain and h*rt that I did. No one understands you. No one cares how your day is going. No one bothers to get to know you as anything more than a nerd, a geek, a loser. You can do nothing for their social status, save the occasional boost to the ego they get from putting you in your place. Some of you, like Chloe Strum, will find outlets in music. Some, like Matthew Ohlson, will have an escape in Dr*gs. Some, like Hailie Duncan, will live their lives pursuing unicorns that they will never, ever catch. I never had a talent to lose myself in, or a dream or unicorn to chase, and so I have taken the path most dreaded. Some of you may soon join me, and I look forward to welcoming a brother or sister to the land where you will never su*fer the loneliness and rejection that faces you now.Farewell forever. I am going to another place. Where, I do not know. But logic dictates that it can only be an improvement. Perhaps my passing will only prove a footnote in a school yearbook. Then again, perhaps the sacrifice of one might bring hope to others. If my d*ath makes life for one person a little more bearable, or a little more enlightened, do I really d*e in vain?“The needs of the many outweigh the needs of the few, or the one.”

Solve the equation. Make sure to explain all of your steps.
1/4 (y + 24) = 32

Please help !!!!!!!!!!!

When Lucy was one month old her grandparents put $25
into a safety deposit box. The next month they put $30,
followed by $35 the month after that. They continued
adding money like this, each month adding $5 more than
the previous month. Her grandparents told her they would
continue doing so until her 18th birthday, at which point
she could use the money to attend college.
a) How much was added into the deposit box on
Lucy’s 10th birthday?
b) How much was added for the final deposit on
Lucy’s 18th birthday?

And

Luke’s father has told him that if Luke walks around the
neighborhood for a whole day to pick up trash then he will
pay him for doing so. He will pay Luke $0.20 for the first
piece and increase the pay by 5% for each piece after that.
This way Luke will get paid more for the pieces that are
harder to find. (round answers to the nearest penny)
a) How much money will Luke be paid for his 100th
piece of trash?
b) If Luke picks up 150 pieces total, then what is the
payment he receives for that final piece?

And

Rewrite the series in summation notation and find the total sum.
-2+1+4+7+….+88

what divided by 6 = 1.2

Please help me solve this!!

Use the numbered angles in the diagram to answer the question.



Which angles form vertical angles?

38 boys and 22 girls visit the zoo 33 of these children have a voucher twice as many boys as girls do not have a voucher

easy 20 points please tell me if I got it right and if not please tell me the right answer

LaTanya will walk her bike from her house to the bike shop, which is 1.5 mi from her house, to get the bike fixed. She expects to wait 30 min for the repair. Then she will ride her bike home. Can she be home in one hour?

BC=CD what is the property

Solve for b.
r=3(b + a)

A pound of ground beef costs $5. At this rate, what is the cost of 1/4 pounds?

Diego is 165 cm tall. Andre is 1.7 m tall. Who is taller, Diego or Andre? 1 m = 100 cm.

1. A multi-cab starter motor has a current of 60.0 A and a voltage of 12 V. What is
the resistance of the starter motor?
А
Given: Current (1)
Voltage (V)
Required: Resistance (9)
V
Formula:
R= voltage
curent
Solution:
V - IR
Answer:
Resistance -
92, the resistance of the electric motor.​

If I was asked to think of a number and multiply it by 2, I could
write this algebraically as 2x.
Write the following algebraically, using x as your unknown.
"I think of a number, multiply it by 3 and add 1 to the result."

-2, 1, 4, 7, 10
find next two term​

2+2(-3)^2


Plz answer :) with steps

Michelle is having a poster printed from a picture that is 4 inches wide by 6 inches tall. The enlarged poster is 20 inches wide and 30 inches tall. Which proportion can be used to represent the picture sizes?
StartFraction 6 over 4 EndFraction = StartFraction 20 over 30 EndFraction
StartFraction 4 over 6 EndFraction = StartFraction 20 over 30 EndFraction
StartFraction 4 over 6 EndFraction = StartFraction 30 over 20 EndFraction
StartFraction 4 over 30 EndFraction = StartFraction 6 over 20 EndFraction

Click and drag the pink tiles to the correct location on the graph organizer.

Aisle 2 of furniture store stocks 4-legged chairs, 4-legged tables and 3 legged stools. Which expressionS shows the total number of furniture legs in aisle 2.
THERE ARE MULTIPLE ANSWERS.

A. 4t+4c+3s
B. 4t+4c+4s
C. 4(t+c) + 3s
D. 4(t+c+s)
E. T+c+s
F. T+c+3s

2.
On Fridays at the ballpark, a cup of soda costs $2, and each refill costs $0.50. If x represents the number of refills, which of the
following equations represents the amount a person spends on soda?
OA. y = 0.5x + 2
OB. y = 2x + 2.5
OC. y=2x+0.5
OD.y=0.5x + 2.5
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I need help with this so can someone please help me

solve x then find each angle measure

Which expression can be used to convert 22 Australian dollars to US dollars?
Assume 1.2 Australian dollars equals 1 US dollar.

;-; I like cheese.....