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## ksaimouli one year ago simplyfy

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1. ksaimouli

$0.2=\cos(\frac{ \pi t }{ 12 })$

2. ksaimouli

solve for t

3. Jonask

$\frac{\pi t}{12}=\arccos (0.2)$

4. ksaimouli

oopss i did not think this way thx

5. Jonask

but are you allowed to use calculator $\pi t/12=\pm \arccos(0.2)+2 \pi k,\forall k\in Z$

6. ksaimouli

i got 5.231 but i only got one what about other value

7. ksaimouli

|dw:1359586504389:dw|

8. ksaimouli

@Jonask

9. Jonask

notice that there are infinite number of solutiond but the general solution of these is $\huge t=\frac{12}{\pi}\arccos(0.2)+2\pi k$ where k can be chosen from interger k={....-2,-1,0,1,2,3,4...}

10. ksaimouli

where that +2 pi k came from

11. Jonask

this is for every period of cos wich is every 360 =2pi but if you never did it just consider your answer + and -5.321 and 360-5.321

12. ksaimouli

but the answers are +5.321 and 18.767

13. Jonask

first $\frac{t \pi}{12}=\cos^{-1}{0.2}=78$

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