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## lilsis76 2 years ago is x=15 degrees a solution of (( sqrt3)/3) cos2x+sin2x=1? how can i figure this out?

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1. campbell_st

just substitute x = 15 into each trig ratio and use the exact angle identities below |dw:1352142650262:dw| if x =15 then 2x = 30.... use the exact values from the triangle above for cos2(15) = cos(30) ans sin2(15) = sin(30)

2. lilsis76

how did you figure the triangle? even i didnt get or understand how to do that

3. lilsis76

is the cos sqrt 3 / 2 and the sin 1/2?

4. campbell_st

its called the an exact value triangle and its usually taught during a topic on trigonometry. thats correct now substitute those values to show that you will get 1 as the answer,

5. lilsis76

okay let me try it. hold on

6. lilsis76

|dw:1352143377873:dw|

7. lilsis76

is this right? so it doesnt equal 1

8. campbell_st

not quite |dw:1352143232742:dw|

9. lilsis76

so it doesnt equal 1 still. right?

10. campbell_st

yes it does you need to check the 1st part |dw:1352143563524:dw|

11. lilsis76

hold on let me try again, i wrote all sloppy

12. lilsis76

|dw:1352144119351:dw|

13. campbell_st

your question says |dw:1352143923416:dw|

14. lilsis76

yes

15. campbell_st

substituting the exact values gives |dw:1352143978828:dw|

16. lilsis76

okay i see the 2x, is basically that value of cos that is the sqrt 3 /2

17. campbell_st

thats right it x = 15 2x = 30 so you are using cos(30) and sin(30) which are known as exact values.

18. lilsis76

|dw:1352144487645:dw|

19. campbell_st

no |dw:1352144327997:dw|

20. lilsis76

okay so the answer is 1/2, so the equation does not equal 1

21. campbell_st

I'll write it again |dw:1352144410590:dw|

22. lilsis76

okay, so i would cross multiply to the the 6/6 to equal 1?

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