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Maths Trig question

Not quite sure how to work this question out, does anyone have any ideas?
θ is obtuse and sin θ= 7/25. Write down the values of cos θ and tan θ


Thanks:smile:))
Original post by jasmine_GCSE
Not quite sure how to work this question out, does anyone have any ideas?
θ is obtuse and sin θ= 7/25. Write down the values of cos θ and tan θ


Thanks:smile:))


Well what do you already know about an obtuse angle? It's between 270 and 360 degrees.

Try working out 7/25, and then pressing the /shift,sin/ button on your calculator to find θ. Once you've done that, you can find cos θ and tan θ.

Hope that helps :smile:
Reply 2
Original post by jasmine_GCSE
Not quite sure how to work this question out, does anyone have any ideas?
θ is obtuse and sin θ= 7/25. Write down the values of cos θ and tan θ


Thanks:smile:))

Start by assuming that θ\theta is acute so draw a right angled triangle with an acute angle θ\theta and label the sides then work out what cosθ\cos \theta and tanθ\tan \theta are.

Then think about how to extend this to an obtuse angle (use CAST/the graph etc.).
Reply 3
Original post by iTzYoBoY
Well what do you already know about an obtuse angle? It's between 270 and 360 degrees.

Try working out 7/25, and then pressing the /shift,sin/ button on your calculator to find θ. Once you've done that, you can find cos θ and tan θ.

Hope that helps :smile:

A question like this would normally say "without using a calculator". Also a calculator may not give your final answer in exact form.
Original post by jasmine_GCSE
Not quite sure how to work this question out, does anyone have any ideas?
θ is obtuse and sin θ= 7/25. Write down the values of cos θ and tan θ


Thanks:smile:))


This is a classic C3 question, that i come across often. It is not as hard as it seems.

1.Draw out a triangle
2.Pick out θ
3. Since Sine is Opposite over Adjacent. Lable the opposite of θ and the Adjacent of θ with your values 7 and 25.
4.Use Pythagoras to work out the side that doesn't have a number on it.
5.Since cosine is Adjacent over hypotenuse. you can work out the value of cos θ
6. to work out tanθ, you already know it is sinθ/cosθ
there fore you can divide your value for sinθ with your value for cosθ

thats how you do it
Original post by joyoustele
...


It's my go-to method for these types of questions, but the one thing you're forgetting is the fact that one should consider that since θ\theta is obtuse, we have 90<θ<18090< \theta < 180 and in this region we have sinθ>0\sin \theta > 0, cosθ<0\cos \theta < 0 and so tanθ<0\tan \theta < 0 which is important for getting the signs right, as the diagrams do not take this into consideration due to lengths being positive.
Original post by RDKGames
It's my go-to method for these types of questions, but the one thing you're forgetting is the fact that one should consider that since θ\theta is obtuse, we have 90<θ<18090< \theta < 180 and in this region we have sinθ>0\sin \theta > 0, cosθ<0\cos \theta < 0 and so tanθ<0\tan \theta < 0 which is important for getting the signs right, as the diagrams do not take this into consideration due to lengths being positive.


Yes.True. Looks like I have just learnt something new. lol
(edited 6 years ago)
Reply 7
Original post by username3585844
Well what do you already know about an obtuse angle? It's between 270 and 360 degrees.

Try working out 7/25, and then pressing the /shift,sin/ button on your calculator to find θ. Once you've done that, you can find cos θ and tan θ.

Hope that helps :smile:

An obtuse angle has a measurement greater than 90 degrees but less than 180 degrees. However, A reflex angle measures more than 180 degrees but less than 360 degrees. ur wrong dude
Original post by joyoustele
This is a classic C3 question, that i come across often. It is not as hard as it seems.

1.Draw out a triangle
2.Pick out θ
3. Since Sine is Opposite over Adjacent. Lable the opposite of θ and the Adjacent of θ with your values 7 and 25.
4.Use Pythagoras to work out the side that doesn't have a number on it.
5.Since cosine is Adjacent over hypotenuse. you can work out the value of cos θ
6. to work out tanθ, you already know it is sinθ/cosθ
there fore you can divide your value for sinθ with your value for cosθ

thats how you do it


This method is wrong, θ is obtuse so you can't apply Pythagoras to the triangle as it won't be a right angle triangle. (Not to mention Sine is opposite over hypotenuse not opposite over adjacent).

Use the identity 1 - sin^2(θ) = cos^2(θ) to get:
cos^2(θ) = 1 - 49/625 = 576/625
cos(θ) = +/- 24/25
Now since θ is obtuse (90º < θ < 180º) the value for cos must be negative so:
cos(θ) = -24/25
And since tanθ = sinθ/cosθ:
tanθ = (7/25) / (-24/25) = -7/24

Voila
Reply 9
Original post by finnyoungman
This method is wrong, θ is obtuse so you can't apply Pythagoras to the triangle as it won't be a right angle triangle. (Not to mention Sine is opposite over hypotenuse not opposite over adjacent).


Please don't resurrect 5 year old threads, and please read the forum guidelines for the Maths forum - in particular, we do not post complete solutions, only hints so that the OP can do the work themselves :smile:

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