Exact Values... (1 Viewer)

[Smile12345]

Hello Everyone...

Could someone please help me with....

Q1. Find the exact value of sec 225 deg.
Q2. Find the exact value of cosec 300 deg.

First thing I tend to do is place it in the difference quadrants... So Q1 would be in Quad 3 (or where T is positive) 45 degrees from 180...

Thanks for your help in advance, it is much appreciated.

 

[pdang]

for q1 first find sec(45) then determine whether it would be +ve or -ve based on quadrants.
same for q2

 

[HeroicPandas]

 

[bedpotato]

1. sec = 1/cos
sec(225) = 1/cos(225) -----> 225 = 180 + 45
sec(180+45) = 1/cos(180+45) -------> cos(180+x) = -cos(x)
sec(180+45) = -1/cos(45) ( cos(45) = 1/sqrt(2) -----> 1/cos(45) = sqrt(2) )
sec(180+45) = -sqrt(2)

Do the same thing for 2.

 

[Smile12345]

Thanks HeriocPandas.... I have remembered this, (I think I must be doing something wrong on mi calc...)

Does it equal -Cos45.... ??

 

[Smile12345]

1. sec = 1/cos
sec(225) = 1/cos(225) -----> 225 = 180 + 45
sec(180+45) = 1/cos(180+45) -------> cos(180+x) = -sin(x)
sec(180+45) = -1/sin(45) ------> sin(45) = 1/sqrt(2) -----> 1/sin(45) = sqrt(2)
sec(180+45) = -sqrt(2)

Do the same thing for 2.

Thanks heaps.... Do you need all these steps? I just did Sec225 = -Cos45 (Using quad for +-, then recip ratio (cos/sec)...Instead of a/h it was h/a....

Can someone please help me here? Am I right or not??

 

[bedpotato]

Thanks heaps.... Do you need all these steps? I just did Sec225 = -Cos45 (Using quad for +-, then recip ratio (cos/sec)...Instead of a/h it was h/a....

First of all, sec(225) =/= -cos(45)
Put 1/cos(225) into your calculator and you get -1.414...
Put -cos(45) into your calculator and you get -0.707...

Secondly...this is going to sound pretty stupid but, idk, lol, sorry...
The steps I've shown you is how I always do (and set out) these types of questions. You don't have to include the working out after the arrows (it wouldn't hurt if you did though), I just did that. You also don't have to include all the sec(180+45).

Try the second question and I'll see if I can help you from there. Don't really understand what you did with the first question (sorry).

 

[Smile12345]

First of all, sec(225) =/= -cos(45)
Put 1/cos(225) into your calculator and you get -1.414...
Put -cos(45) into your calculator and you get -0.707...

Secondly...this is going to sound pretty stupid but, idk, lol, sorry...
The steps I've shown you is how I always do (and set out) these types of questions. You don't have to include the working out after the arrows (it wouldn't hurt if you did though), I just did that. You also don't have to include all the sec(180+45).

Try the second question and I'll see if I can help you from there. Don't really understand what you did with the first question (sorry). That's allright.

I would go like this for the second one... I would put it on a diagram... In the 4th Quad, 60 deg from the 0/360 line... Then this is 300degT or Cosec300... = Sin60 (relative angle)... Cosec being the recip trig ratio of Sin... Then Cosec300 = - Sin60 because Sin is negative in the 4th Quad (only Cos is positive)... This probably doesn't make sense to you...

Thanks for your patience.

 

[Smile12345]

Sorry, my previous answer wasn't complete Sin60 = opposite/hypotenuse so instead because it's cosec, it would be hypotenuse/opposite.... Which would equal 2/root 3 and -2/root 3 because it's in the 4th quadrant.

 

[Smile12345]

I think I'm confusing myself here.... I appreciate everyone's help so far (but esp. bedpotato! )... Thanks.

 

[Smile12345]

I will +1 to your rep bedpotato....

Could you write out the way you do Q2? I need to learn this way...

 

[bedpotato]

Don't worry, I get it. This is the time of the night where my brain starts to slow down.
What you're doing is right. But remember cosec = 1/sin
So cosec(300) = -1/sin60
You only wrote cosec(300) = -sin60.

You made the same mistake for the first question.
You said sec(225) = -cos(45)
But remember: sec = 1/cos
So:
sec(225) = -1/cos(45)

Is it a bit clearer now?

 

[bedpotato]

Sorry, my previous answer wasn't complete Sin60 = opposite/hypotenuse so instead because it's cosec, it would be hypotenuse/opposite.... Which would equal 2/root 3 and -2/root 3 because it's in the 4th quadrant.

Yep, you're right.
So:
cosec(300) = -1/sin(60) ----> which = -2/sqrt(3)

 

[Smile12345]

Don't worry, I get it. This is the time of the night where my brain starts to slow down. Yeah, I think maybe mine too!
What you're doing is right. But remember cosec = 1/sin
So cosec(300) = -1/sin60
You only wrote cosec(300) = -sin60.

You made the same mistake for the first question.
You said sec(225) = -cos(45)
But remember: sec = 1/cos
So:
sec(225) = -1/cos(45)

Is it a bit clearer now?

Yes, that is clearer thanks.

I'll do one more so if it was.... Q. Find the exact value of cos(-30)...

So Cos (-30) = 2/root3... I suppose this is a bit different, not really like the last two.

Thanks...

 

[bedpotato]

Yes, that is clearer thanks.

I'll do one more so if it was.... Q. Find the exact value of cos(-30)...

So Cos (-30) = 2/root3... I suppose this is a bit different, not really like the last too.

Thanks...

Try this: sec(240)

 

[girlworld_club]

in your working you wrote cos(180+x) = -sin(x)

just wondering why you did this..i thought
cos(x) = cos(180 + x)

 

[Smile12345]

Try this: sec(240)

sec(240) = -1 / cos(60) --------> -2/1 = -2

This right?? Thanks ...

 

[bedpotato]

in your working you wrote cos(180+x) = -sin(x)

just wondering why you did this..i thought
cos(x) = cos(180 + x)

I made a mistake. It's actually cos(180+x) = -cos(x) --> since it's in the third quadrant where only tan is positive. Sorry about that.
But I still got the answer because cos(45) = sin(45) --> If it was 30 or 60 degrees, then I would've gotten it wrong.
Thanks for pointing that out. I've fixed it now.

sec(240) = -1 / cos(60) --------> -2/1 = -2

This right?? Thanks ...

Yep, that's right.

 

[koreafantasy]

Step 1- convert your secs and cosecs into 1/cos and 1/sin
Step 2- Type 1/cos225 and 1/sin300 into calculator
Step 3- press equal sign
Step 4- square it.
Step 5- Root that using square root signs, instead of your calculator

Screw the quadrant bs, exact value tables etc... easy, sure-way method which given enough practise, you can memorise that 0.86.....etc is root3 / 2, 0.71... etc is 1/ root 3 and so on haha

 

[Smile12345]

Step 1- convert your secs and cosecs into 1/cos and 1/sin
Step 2- Type 1/cos225 and 1/sin300 into calculator
Step 3- press equal sign
Step 4- square it.
Step 5- Root that using square root signs, instead of your calculator

Screw the quadrant bs, exact value tables etc... easy, sure-way method which given enough practise, you can memorise that 0.86.....etc is root3 / 2, 0.71... etc is 1/ root 3 and so on haha

Yeah gotcha. Sure... Will be doing.