Is the answer to: cosθ, if tanθ = 1 and 180° < θ < 270° ; (√ 2)/2 ?
close, but remember that in the third quadrant the cosine is negative, so
cosØ = -√2/2
To find the value of cosθ, we can use the given information that tanθ = 1 and 180° < θ < 270°.
First, let's recall some trigonometric identities:
1. tanθ = sinθ/cosθ
2. cos²θ + sin²θ = 1
Using the first identity, we know that tanθ = sinθ/cosθ = 1. Rearranging this equation, we get sinθ = cosθ.
Now, we can use the second identity to find the value of sinθ.
cos²θ + sin²θ = 1
Since sinθ = cosθ, we can substitute it into the equation:
cos²θ + (cosθ)² = 1
2cos²θ = 1
cos²θ = 1/2
cosθ = √(1/2) = √2/2
Therefore, the value of cosθ, given that tanθ = 1 and 180° < θ < 270°, is indeed (√2)/2.