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# another trig.... watch

1. ok - i've now decided that I'm not having a "good trigonometry day" today!

Express (12 cos θ - 5 sin θ) in the form R cos (θ+α) where R > 0 and 0<α<90°

thank you for any replies..... (lets hope they don't run away this time - Re:dvs)

Laura xxxx
2. (Original post by Laura_M)
ok - i've now decided that I'm not having a "good trigonometry day" today!

Express (12 cos θ - 5 sin θ) in the form R cos (θ+α) where R > 0 and 0<α<90°

thank you for any replies..... (lets hope they don't run away this time - Re:dvs)

Laura xxxx

R = √(12²+5²) = 13

13cosα = 12
cosα = 12/13
α = 22.6°

(12 cos θ - 5 sin θ ) = 13cos(θ + 22.6)
3. thanks a lot !

How do I rep someone? (e.g. you!)
4. click on the weighing scales in the top right corner of my post.
(feels good to be appreciated)
5. hmmm.... why does 13 cos α = 12 ???
6. acosθ +bsinθ

R = √(a²+b²)

R cosα = a
R sinα = b

some books use:
tanα = b/a

its just the rule
7. If you want a proper explanation:

12 cos θ - 5 sin θ = R cos ( θ+α )
_ _ _ _ _ _ _ _ _ = R cosθcosα - R sinθsinα (by compound angle formula)

Therefore, equating the different terms: 12 cos θ = R cosθcosα , so R cosα = 12
_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _5 sin θ = R sinθsinα , so R sinα = 5

Treat the statements in bold as simultaneous equations. If you square both of them and add them, you get
R^2 sin^2 α + R^2 cos^2 α = 12^2 + 5^2
R^2 ( sin^2 α + cos^2 α ) = 144 + 25
And since sine squared plus cos squared equals one....
R^2 = 169
R = 13

To get alpha, do "R sinα = 5" / "R cosα = 12"
i.e.:
R sinα ` ` 5
------ = --
R cosα ` 12

R tanα = 5/12

α = tan^-1 (5/12)
8. yeah... whatever he says
9. (Original post by Undry1)
yeah... whatever he says
I use the exact method that "he" uses. It is the proper way.

[ well they are identical, except the second requires no remembering of rules ]
10. now I'm seriously thinking about giving up...... lol

Solve, 8 cot θ - 3 tan θ = 2

0<θ<90°

all your replies are greatly appreciated - sometimes it helps to see different explanations - it makes me understand it better

Laura xxxx

editted: ok sorry, I've done it now. I should try for longer before I give up!!

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