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pls help trig functions

hey can ne1 help me! im lost!!!

a) prove that for all values of x,
sinx + sin(60+x)= sin(60+x)
b) given that sin84 - sin36 = siny find the value of the acute angle y

solve
2sin2x+sin(60-2x)=sin(60+2x)-1
for values of x in the interval 0-360, answer 2 one decimal place (all angles in degrees)

i jus dont know were to satrt! cheers

Reply 1

arktos

remember that sin (a+b) can be expanded in terms of sin and cosine; sin (a+b) = sinacos b + sinbcos a, and that sin84 - sin 36 can be written as sin(60+24) - sin (60-24)

dont know if this helps, I hate trig proofs soo much. good luck

Reply 2

shazzacon

thanks yeah i was tryin it that way but i cldnt get it 2 equal!!! an i tried it a diff way an ended up wit cos(x-30) lol

Reply 3

C4>O7

shazzacon

a) prove that for all values of x,
sinx + sin(60+x)= sin(60+x)

sinx + sin(60+x) = sin(60+x) ==> sinx = 0
This can't be an identity :confused:

Reply 4

bob_54321

yeh, it isn't true for all values of x at all, have you copied it down wrong?

Reply 5

shazzacon

bob_54321

yeh, it isn't true for all values of x at all, have you copied it down wrong?

sinx + sin(60-x) = sin(60+x)

sorry that was my mistake!! still im confused!

Reply 6

davros

Start by expanding sin (60-x) using the standard formula. What do you get when you add sin x to this?

That will get you started!

Reply 7

steve2005

shazzacon

sinx + sin(60-x) = sin(60+x)

sorry that was my mistake!! still im confused!

Here is solution.

Picture 24.png31.6KB

Reply 8

carol05

shazzacon

b) given that sin84 - sin36 = siny find the value of the acute angle y

Unparseable latex formula:

[br]\[br] \sin 84 - \sin 36 = \sin y \\ [br] \sin A - \sin B = 2\cos (\frac{{A + B}}{2})\sin (\frac{{A - B}}{2}) \\ [br] \sin 84 - \sin 36 = 2\cos 60\sin 24 \\ [br] ......................= 2(0.5)\sin 24 \\ [br] ......................= \sin 24 \\ [br] ..................y = 24 \\ [br] \\ [br] \[br]\

Reply 9

steve2005

shazzacon

solve
2sin2x+sin(60-2x)=sin(60+2x)-1
for values of x in the interval 0-360, answer 2 one decimal place (all angles in degrees)

I don't see why they asked for angles to 1 decimal place. The angles come out as exact whole numbers !

Picture 27.png22.1KB

Reply 10

shazzacon

steve2005

I don't see why they asked for angles to 1 decimal place. The angles come out as exact whole numbers !

cheers thanks every1 for helpin me i really am useless with these trig things!!they are so hard an u hav 2 learn everythin guess im jus gonna hav to kepp tryin but every1 is brill on here so cheers an il prob b back soon lookin 4 help!!

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