Trig problem sin(Ø + pi/4)

[lanieley]

Trig problem sin(Ø + pi/4)

Everyone was so helpful today so I thought I'd ask another question.

This is a non calculator problem.
I got part a but I don't understand part b.

If cosØ= -5/13 and sinØ >0 find the exact value of:
a) cotØ
The answer I came up with is that Ø is in Quadrant 2 and CotØ = -5/12

b)sin(Ø + ?/4)

This is where I am stuck.

 

[soroban]

Re: Trig problem sin(Ø + pi/4)

Hello, lanieley!

\(\displaystyle \text{If }\cos\theta \,=\,-\frac{5}{13}\,\text{ and }\,\sin\theta \,>\,0\)

\(\displaystyle \text{find the exact value of: }\;a)\;\cot\theta\)

\(\displaystyle \text{The answer I came up with is: }\:\theta\text{ is in Quadrant 2 and }\cot\theta \:=\:-\frac{5}{12}\) . . . . Right!


\(\displaystyle b)\;\sin\left(\theta + \frac{\pi}{4}\right)\)

\(\displaystyle \text{Use: }\:\sin(A + B) \;=\;\sin A\cos B + \sin B\cos A\)

\(\displaystyle \text{Then: }\;\sin\left(\theta + \frac{\pi}{4}\right) \;=\;\sin\theta\cos\frac{\pi}{4} + \sin\frac{\pi}{4}\cos\theta \;=\;\frac{\sqrt{2}}{2}\sin\theta + \frac{\sqrt{2}}{2}\cos\theta\)

 

[lanieley]

Re: Trig problem sin(Ø + pi/4)

Thank you.
I wonder if that is all the answer is suppossed to be.

 

[Deleted member 4993]

Re: Trig problem sin(Ø + pi/4)

Thank you.
I wonder if that is all the answer is suppossed to be.<<< Why do you wonder - what does your class notes say

What was the value of

\(\displaystyle \sin\theta\\\)

that you found previously - use that.

 

[lanieley]

Re: Trig problem sin(Ø + pi/4)

What was the value of sin? that you found previously - use that.

..hm..! Yes that might work except -the question reads Sin (? + ?/4) not Sin(?) + ?/4
Plus it's a non calculator section so I can't use the sides to figure out ?.

I looked in my exercise book for simaliar questions and they all left their answers in terms of ? so I think I should be okay. Thanks for your help =D

 

[Deleted member 4993]

Re: Trig problem sin(Ø + pi/4)

What was the value of sin? that you found previously - use that.

..hm..! Yes that might work except -the question reads Sin (? + ?/4) <<< I don't think you have understood Soroban's solution. Don't just stare at the screen - take paper and pencil and work it out - following his method.


not Sin(?) + ?/4
Plus it's a non calculator section so I can't use the sides to figure out ?.

I looked in my exercise book for simaliar questions and they all left their answers in terms of ? so I think I should be okay. Thanks for your help =D