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!

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S\ 1\<-- off h~ pSin A = ----=:;-+-L.-_

-CA--~Cos A = ~.()..._d.~~....-_

hjP

Ex 1) Find sin Band cos B:S,(1 ~ -.:::ofe

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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\-\)

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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