Question

If Tan θ = – ½ and the terminal side of the angle is in the IIQuadrant, then Cos θ =

Answer 1

Step-by-step explanation:

p b p

h h b

Tan theta is 1/2

Means - P =1 ,B = 2

then cos is b/h

finding H

H²= B²+P²

H² = 2)² + (1)²

H²= 4+1

H =√5

Cos = B/H

Cos theta = 2/√5

Answer 2

The value of

$\cos(θ) = - \frac{2}{ \sqrt{5} }$

GIVEN

$\tan(θ) = - \frac{1}{2}$

The terminal side of the angle is II quadrant.

TO FIND

The value of

$\cos(θ)$

SOLUTION

We can simply solve the above problem as follows -

It is given ,

Terminal side of the angle is in second Quadrant-

The value of θ can be between 90° and 180°.

Therefore,

$\cos(θ) <0$

And,

$\sin(θ) >0$

We know that,

$\tan(θ) = \frac{ \sin(θ) }{ \cos(θ) } = - \frac{1}{2}$

And,

${ \cos^{2} (θ) } + \sin^{2} (θ) = 1$

So,

$\sin^{2} (θ) = 1 - \cos^{2} (?)$

$\cos^{2} (θ) + ( - \frac{1}{2} \cos(θ) )^{2} = 1$

$\cos^{2} (θ) = - \frac{4}{5}$

$\cos(θ) = - \frac{2}{ \sqrt{5} }$

Hence, The value of

$\cos(θ) = - \frac{2}{ \sqrt{5} }$

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