Question

What is the Exact value of sin θ / 2, cos θ = -4/5, θ is quadrant 3

Answer 1

Do you mean \(\sin\left(\frac{\theta}{2}\right)\) or \(\frac{\sin\theta}{2}\)?

Answer 2

\[\sin \frac{\theta}{2}=\pm\sqrt{\frac{1-\cos\theta}{2}}\]
Since \(180\leq\theta\leq 270, 90\leq\frac{\theta}{2}\leq135\) and therefore, the correct sign to choose is +.
Now just plug in the value of cos(theta).

Answer 3

how do i get the value of cos(tetha)?

( i am completely lost in this lesson)

Answer 4

It's in your very first post.

Answer 5

it gives me "0.316227766" is that correct?

Answer 6

cosx=1-2sin^2 (x/2)
-4/5 = 1-2sin^2 (x/2)
-9/5 = -2sin^2 (x/2)
9/10 = sin^2 (x/2)
sin(x/2)= sqrt(9/10) or -(sqrt(9/10)
sin=-ve at quadrant 3
therefore, sin(x/2) = -(sqrt(9/10)