Question

Please help me !! Thank you !!!!

Answer 1

Explanation:

so this involves a big long formula.. I suspect that if you look at the video it will tell you the formula you need. or you can look up laws of addition for sin. it's very common but also complex. So I can see why you've posted this as a question. look at the video, then put a comment in the comments below if you don't get it okay so in the video they probably give you these formulas which you'll need..

Sin(a+b)=sin(a)cos(b)+cos(a)sin(b)

Cos(a+b)=cos(a)cos(b) - sin(a)sin(b)

now we need to figure out what cos(Ф) is and what cos(∅) is ( we're given sin of both ) and we're told they are in the 2nd quadrant.. which means that the fractions have a negative sign on them both

Ф=theta

∅= phi

to find Cos(Ф) use 1=
`Cos^(2)`(Ф) +
`Sin^(2)`(Ф)

use your algebra skills to solve for Cos(Ф)

√(1-
`Sin^(2)`(Ф) ) = Cos(Ф)

√( 1 - (
`(20)/(29)`)^2 ) = Cos(Ф)

√( 1 - 400/841) = Cos(Ф)

√( 441/841 ) =Cos(Ф)

√441 / √841 = Cos(Ф)

21/29 = Cos(Ф)

now the same long process for Cos(∅)

√(1-
`Sin^(2)`(∅) ) = Cos(∅)

√( 1 - (
`(8)/(17)`)^2 ) = Cos(∅)

√( 1 - 64/289) = Cos(∅)

√( 225/289) = Cos(∅)

√225 / √289 = Cos(∅)

15 / 17 = Cos(∅)

now we can finally plug in the known values of

sin(Ф) = - 20/29 (b/c this is in the 2nd quad it's negative)

sin(∅) = - 8/17 ( same as above)

cos(Ф) = - 21/29 ( same as above)

cos(∅) = - 15/17 ( same as above)

into those addition formulas above, here they are again

Sin(Ф+∅)=sin(Ф)cos(∅)+cos(Ф)sin(∅)

Sin(Ф+∅)= (-20/29)(-15/17) + (-21/29)(-8/17)

Sin(Ф+∅)= 300/493 + 168/493

Sin(Ф+∅)= 468/493

that's the 1st answer... I told you this is long :/ now we need this formula

Cos(Ф+∅)=cos(Ф)cos(∅) - sin(Ф)sin(∅)

Cos(Ф+∅= (-21/29)(--15/17) - (20/29)(-8/17)

Cos(Ф+∅)=315/493 - 160/493

Cos(Ф+∅)= 155/493

there is the 2nd answer... ask if you need more explanations :?