3.2 notes sine and cosine ratios cosine and sine ratios · 2019. 11. 29. · 3.2 notes sine and...
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Math 10
3.2 Notes
Sine and Cosine Ratios
Cosine and Sine ratios:
- We have learned about tangent ratios.
- Sine and Cosine ratios follow the same process except they involve the
hypotenuse!
.IDA"
~Q--8Jt l' l'
S\ 1\<-- off h~ pSin A = ----=:;-+-L.-_
-CA--~Cos A = ~.()..._d.~~....-_
hjP
Ex 1) Find sin Band cos B:S,(1 ~ -.:::ofe
\~f
_ ~J..-~-;)lc;
1
You try ....
_ 1,5 -_O~'3~2.,nooo ~_'.,". Q_ 0 i\ -:L \- '-_ Sin D =.~ \ ~ -::: \ ...,. 'Ies ~jf t). S
F cos E= ,ClJj -:: ~. D_ ~O,)FHsinE =\"\JP CO • ~
Finding an angle:
Just like before, we can use the inverse trigonometric ratio to find the angle!
Ex: sin (3= 0.4384 Find (3: .s \ \\ -, ( 0 \ t.t 3~ L-\-')
[~=d-b.OoJ
Ex: cas 8 = 2/10 !=ind8:
COS 9 ~ () ..2_<, Vu\:
e ~ Cos. -\ (0 .L)l8~l~-S-Q\
2
Solving Problems:s-\-Gp S ::I!J 0\ 't C\ \"J 6. 0..(\ ~ \ abe.\
s\o\-e~ \ 0-f\8\esFinding the unknown angle
fP R ~m~'0l ~ x: .so \._\(f1)-t TDftEx 1: . \ I I J
Q tJeG ()\e. uJ \\ \ L'" uJ \'\, n·e '\~ 'I OV\..-
Al J:j ef ght rasts a 15.'- ladder aga j st a build ing. as sho.•,m. SC)\ \le. rVC>b \ -{N\ .'tV at an gle d 25 the ad;.,;2,," a eo with .c grc r d ?G\(2 Y:JU answ-er:o t e .carestd.cgre2.
'~~L ~ tH\\- L \-\\V( hG\ \l e. ().&~ ) njr .U~~ GOS\f\G (Crr\-\)
.--======-
CJJ~ L \~ - (A o'i =- ,y. r_
hjr \'Stb
c.OS L \-\ ~ 0, S41-\~-lL .\-\= co s-\ (0 ' s 4 '-\-«)\ ')
\LM =~i-:\Using cosine and sine ratios to find unknown lengths
Ex 2: Find the length of RSto the nearest tenth of a metre.()..(,\j
R ~_ S.'opo ./."..r .>..g.~ l
~./ \-\jP'
So \-\ C~ \-\-
Ex 3: A skier races 3514 m down a ski hill. The ski course meets the ground at anangle of 16°. What is the vertical height of the course?
S\(.\' "hjfJ J
1Cou.v~e..,
fy:: ~ ~ 3~5-,--=-\_L\ ~\'Y\_ \'<1
~ '\"()'v\<' eX. .<; l cu\) )
s\X'\ \~O:;::.. O?~_3S\i\
s\(\\10Q i- 3 5 \ 1-\ - o_p-p-------.o :).r-51o 1-- 35 \L-\ ::: \ ~ loB ~6 m \
~\ lA\1 e..) L -=- \b o
L \(jP -= 3 5 \qv- It\~a.n\--- opp
How to deal with any problem: ttV)pO\='Q J
Draw yourself a triangle given any known dimensions and angles.- Label all sides (opp, ad], hypotenuse) cg\S- Then decide which trig ratio will let you answer the question
o Remember SOH CAH TOA !
If you are looking for a length, use the ratio e. -c : .:s \ {\ e =- \,~~If you are looking for an angle, use the inverse ratio u
'-----------------...:::...!::.-~ =- S\(\- \ ( ~)
Do Text Q'5: p. 120 #1-9
Challenge? .•. try Q15
4
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