Question

Find cos theta in (pi/2,pi) so that cot theta = -12/5

Answer 1

what?

Answer 2

It is impossible for the value of cosine of any angle to be larger than 1 and smaller than -1. We notiuce that cos theta = -12/5 = -2.4 < -1, therefore there is no value for theta in (pi/2 , pi)

Answer 3

Cot theta...

Answer 4

\[\frac{\text{Sin}[\theta ]}{\text{Cos}[\theta ]}=\frac{-5}{12}\]

Answer 5

Ok, that's tan theta, so what's cos theta?

Answer 6

\[\frac{12}{-5} \text{Sin}[\theta ]=\text{Cos}[\theta ]\]

Answer 7

I want a value...

Answer 8

To find this value, you'll have to apply Pythagorean identity:
1 + (tan theta)^2 = 1/(cos theta)^2
(cos theta) = - sqrt [1/1 + (tan theta)^2]

Answer 9

@giorgia

looks promising, so what is it then?

Answer 10

You'll plug the value for tan theta and you'll raise to square:
(cos theta) = - sqrt [1/1 +144/25]
cos theta = -sqrt169/25
cos theta = -13/5

Answer 11

Nope.

Answer 12

oh, yes!

Answer 13

12/13 ?

Answer 14

Think the problem is us have sqrt(1/1...) instead of

1/sqrt(1+

Answer 15

@imranmeah

Close....check interval.

Answer 16

Sign of cos in second quadrant?

Answer 17

-12/13