# trigonometric identites

• Apr 29th 2009, 06:02 AM
Sundae
trigonometric identites
I need help on this question:

Q) Calculate without using a calculator the exact value of
√3 cos15 - sin15

Ans) √2

can someone show me the working of it. Thx!

(the equation isnt equal to 0 or anything)
• Apr 29th 2009, 06:11 AM
mr fantastic
Quote:

Originally Posted by Sundae
I need help on this question:

Q) Calculate without using a calculator the exact value of
√3 cos15 - sin15

Ans) √2

can someone show me the working of it. Thx!

(the equation isnt equal to 0 or anything)

Use the half angle formulas: 4. Half Angle Formulas
• Apr 29th 2009, 06:27 AM
Sundae
The half angle formula hasnt been introduced in the chapter yet, only the addition formula so i dont think im suppose 2 use it for this question. (and i dont know where to begin wiv tht formula).
• Apr 29th 2009, 06:31 AM
mr fantastic
Quote:

Originally Posted by Sundae
I need help on this question:

Q) Calculate without using a calculator the exact value of
√3 cos15 - sin15

Ans) √2

can someone show me the working of it. Thx!

(the equation isnt equal to 0 or anything)

Quote:

Originally Posted by Sundae
The half angle formula hasnt been introduced in the chapter yet, only the addition formula so i dont think im suppose 2 use it for this question. (and i dont know where to begin wiv tht formula).

cos(15) = cos(45 - 30)

sin(15) = sin(45 - 30)
• Apr 29th 2009, 06:42 AM
Sundae
that just made things more muddled up... buh thx for ur help.
• Apr 29th 2009, 06:48 AM
e^(i*pi)
Quote:

Originally Posted by Sundae
that just made things more muddled up... buh thx for ur help.

What have you covered already? As far as I'm aware the two solutions proposed by Mr F are the best/only methods:

$cos(A \pm B) = cosAcosB \mp sinAsinB$

$sin (A \pm B) = sinAcosB \pm cosAsinB$

unless you're more familiar with that form.
(The half angle formulae are also derived from that form because cosA = cos(0.5A+0.5A))
• Apr 29th 2009, 07:06 AM
Sundae
im using the heineman c3 book, exercise 7A its only covered the additional rule.
• Apr 29th 2009, 03:40 PM
mr fantastic
Quote:

Originally Posted by Sundae
im using the heineman c3 book, exercise 7A its only covered the additional rule.

If you are unable to apply either of the methods I have suggested then you are currently not in a position to be able to do the question at all. In which case you will just have to wait until you have covered that material in class. Then come back and review this thread.
• Apr 30th 2009, 01:11 AM
Sundae
i home school >.< i dont have a teacher i been teaching myself.
• Apr 30th 2009, 02:04 AM
mr fantastic
Quote:

Originally Posted by Sundae
i home school >.< i dont have a teacher i been teaching myself.

Then find the section of your book that has the fomulas given in post #6. Then review this thread. There's no point trying attempting questions that require maths you haven't learned or studied.
• Apr 30th 2009, 02:07 AM
Sundae
i understand what ur saying, i appreciate ur help. I just wanted to see the working out of the question >.<