Question

I NEED HELP PLEASE, THANKS! :)

Answer 1

Answer:

Step-by-step explanation:

Another way of looking at this is

$cos\theta=\frac{1}{2}$, which is a first quadrant angle where x is positive (it could also be a 4th quadrant angle, and it actually ends up there, but either way we'll get to where we're needing to be). The equation asks us to find the angle theta that has a cos of 1/2. We set up the reference angle in quadrant 1. Since cosine is by definition side adjacent over hypotenuse, we put the value of 1 along the x quadrant since that's the side adjacent to the reference angle, and then put the 2 along the hypotenuse of the right triangle that we form. That means that the side across from the reference angle is the square root of 3 which makes the reference angle a 60 degree angle, or pi/3.

So $\theta=\frac{\pi}{3}$

Now we need to find the csc of pi/3 - pi/2. Csc is the inverse of the sin ratio, so we can rewrite it in terms of sin:

$\frac{1}{sin(\frac{\pi}{3}-\frac{\pi}{2}) }$ which simplifies to

$\frac{1}{sin(-\frac{\pi}{6}) }$ after finding a common denominator and subtracting.

$-\frac{\pi}{6}$ is a 30 degree angle measured clockwise from the positive axis, putting that 30 degree angle into quadrant 4. On you calculator, you will find that 1 over the sin of -30 degrees is

-2.

Answer 2

Answer:  b) -2

Step-by-step explanation:

cos θ = 0.5  

$\cos \theta=\dfrac{1}{2}\qquad \rightarrow \qquad \theta =\dfrac{\pi}{3}\\\\\\\csc\bigg(\dfrac{\pi}{3}-\dfrac{\pi}{2}\bigg)\\\\\\=\csc\bigg(-\dfrac{\pi}{3}\bigg)\\\\\\=\csc \bigg(\dfrac{5\pi}{3}\bigg)\\\\\\=\dfrac{1}{\sin (\frac{5\pi}{3})}\\\\\\=\dfrac{1}{-\frac{1}{2}}\\\\\\=\large\boxed{-2}$