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# Trig watch

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1. 3 cos x + cot x = 0

What do I do now?

3 cos x + 1/tan x = 0

Then what?

Thank you

Jorge
2. (Original post by Jorge)
3 cos x + cot x = 0
3cosx + cosx/sinx = 0
3cosxsinx + cosx = 0
cosx[3sinx + 1] = 0
cosx = 0 or sinx=-1/3

3cosxsinx + cosx = 0

thats is cosx(3sinx+1) = 0

DONT FORGET THE cosx=0 else you lose solutions!
4. (Original post by Jorge)
3 cos x + cot x = 0

What do I do now?

3 cos x + 1/tan x = 0

Then what?

Thank you

Jorge
Change to 3cosx + cosx/sinx = 0
get the whole LHS over sin x
get to cosx(3 sinx + 1)/sin x = 0

be careful not to "lose" solutions if you cancel.

Aitch
5. Mm, thanks for the correction.
I haven't done much pure based work since September. Just M2/M3/D1 mainly.
6. seems to be some consensus here then!

Aitch
7. Brilliant

Would you like to do the exam for me?

sqrt3 cot x + 1 = 0

Thanks

Jorge
8. Sorry forget it. I got it

sqrt3/tanx = -1

sqrt3 = -tan x

tanx = -sqrt3

x = 120 or 300

Thanks

Jorge
9. (Original post by Jorge)
Brilliant

Would you like to do the exam for me?

sqrt3 cot x + 1 = 0

Thanks

Jorge
-sqrt3=tanx
10. Another one?

sec(2x - 60) = - 2/sqrt3

1/cos(2x - 60) = - 2/sqrt3

-2 cos(2x - 60) = sqrt3

cos(2x - 60) = - sqrt3/2

(2x - 60) = 150

2x = 210

x = 105

Solutions 105 and (360-105) 255

But the book's solutions are

105, 135, 285, 315

What have I done wrong?

Thanks

Jorge
11. because you have worked out 2x u need to change the limits.
If 0 < x < 360 then for 0 < 2x < 720.
Then u will get 4 answers not 2.
12. Got it, thanks

Jorge
13. One more please, before lunch:

2 tan x = cot x + 1

2 tan x = 1/tan x + 1

2 tan^2 x = 2

tan^2 x = 1

tan x = +/- 1

x = 45 or -45

Angles 45, 135, 225, 315

But the book says: 45, 153.4, 225, 333.4

What did I do wrong?

Thanks
14. 2tanx = cotx + 1
2tanx = 1/tanx + 1
2tanx^2 = 1 + tanx
2tanx^2 - tanx - 1 = 0

let tanx = y

2y^2 - y - 1 = 0
(2y+1) (y-1) = 0
y = -1/2 or y=1

therefore:

tanx = -1/2 or tanx = 1
x= -26.6 x = 45 and (180+45=) 225
= (180+(-26.6))
= 153.4
and (360-26.6=) 333.4

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Updated: January 14, 2005
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