Answer: ![\bold{-\dfrac{7\sqrt2}{10}}](https://tex.z-dn.net/?f=%5Cbold%7B-%5Cdfrac%7B7%5Csqrt2%7D%7B10%7D%7D)
<u>Step-by-step explanation:</u>
It is given that θ is between 270° and 360°, which means that θ is located in Quadrant IV ⇒ (x > 0, y < 0). Furthermore, the half-angle will be between 135° and 180°, which means the half-angle is in Quadrant II ⇒
It is given that sin θ =
⇒ y = -7 & hyp = 25
Use Pythagorean Theorem to find "x":
x² + y² = hyp²
x² + (-7)² = 25²
x² + 49 = 625
x² = 576
x = 24
Use the "x" and "hyp" values to find cos θ:
Lastly, input cos θ into the half angle formula:
![cos\bigg(\dfrac{\theta}{2}\bigg)=\pm \sqrt{\dfrac{1+cos\ \theta}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{1+\dfrac{24}{25}}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{\dfrac{25}{25}+\dfrac{24}{25}}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{\dfrac{49}{25}}{2}}\\\\\\.\qquad \quad =\pm \sqrt{\dfrac{49}{50}}\\\\\\.\qquad \quad =\pm \dfrac{7}{5\sqrt2}}\\\\\\.\qquad \quad =\pm \dfrac{7}{5\sqrt2}}\bigg(\dfrac{\sqrt2}{\sqrt2}\bigg)\\\\\\.\qquad \quad =\pm \dfrac{7\sqrt2}{10}](https://tex.z-dn.net/?f=cos%5Cbigg%28%5Cdfrac%7B%5Ctheta%7D%7B2%7D%5Cbigg%29%3D%5Cpm%20%5Csqrt%7B%5Cdfrac%7B1%2Bcos%5C%20%5Ctheta%7D%7B2%7D%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cquad%20%3D%5Cpm%20%5Csqrt%7B%5Cdfrac%7B1%2B%5Cdfrac%7B24%7D%7B25%7D%7D%7B2%7D%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cquad%20%3D%5Cpm%20%5Csqrt%7B%5Cdfrac%7B%5Cdfrac%7B25%7D%7B25%7D%2B%5Cdfrac%7B24%7D%7B25%7D%7D%7B2%7D%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cquad%20%3D%5Cpm%20%5Csqrt%7B%5Cdfrac%7B%5Cdfrac%7B49%7D%7B25%7D%7D%7B2%7D%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cquad%20%3D%5Cpm%20%5Csqrt%7B%5Cdfrac%7B49%7D%7B50%7D%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cquad%20%3D%5Cpm%20%5Cdfrac%7B7%7D%7B5%5Csqrt2%7D%7D%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cquad%20%3D%5Cpm%20%5Cdfrac%7B7%7D%7B5%5Csqrt2%7D%7D%5Cbigg%28%5Cdfrac%7B%5Csqrt2%7D%7B%5Csqrt2%7D%5Cbigg%29%5C%5C%5C%5C%5C%5C.%5Cqquad%20%5Cquad%20%3D%5Cpm%20%5Cdfrac%7B7%5Csqrt2%7D%7B10%7D)
Reminder: We previously determined that the half-angle will be negative.
A! You need to multiply all the numbers together
I'm too late but here ya go anyway :)
x = 180 - (31 + 40) is the answer.
Answer:
See attached picture.
Step-by-step explanation:
h(x) has two functions in it. It has y = x and y =-x. Both have a slope of 1 or -1 and are diagonal lines. This means only 2 graphs of the four choices are possible answers.
Notice that y = -x has an interval that is greater than or equal to. This means it is marked with a closed or filled in dot at its start. This means choice B is the correct choice.
5 times 2/6 is 10/6
You can simplify that to 5/3