Question

For 0° ≤ x < 360°, what are the solutions to sin(StartFraction x Over 2 EndFraction) + cos(x) – 1 = 0 ?

{30°, 150°}
{60°, 300°}
{120°, 240°}
{210°, 330°}

Answer 1

Question:

What value of x satisfies cot ( 90° - x ) = - sqrt 3/3 ?

Answer:

D. 150°

Explanation:

I got it correct in my test :)

Answer 2

{60°, 300°}

Using the half angle identity:

$\sin\left(\frac{x}{2}\right)+\cos\left(x\right)-1=0\\\sin\left(\frac{x}{2}\right)+1-2\sin^{2}\left(\frac{x}{2}\right)-1=0\\\sin\left(\frac{x}{2}\right)-2\sin^{2}\left(\frac{x}{2}\right)=0\\\sin\left(\frac{x}{2}\right)\left(1-2\sin\left(\frac{x}{2}\right)\right)=0$

Using zero product rule:

$\sin\left(\frac{x}{2}\right)=0,\frac{1}{2}\\x=\frac{x}{2}=0,30,150,180\\x=0,60,300,360$

Since, 0° ≤ x < 360°, so, x=60,300

Learn more about half angle: https://brainly.com/question/2254074