Question

Solve (2cos² y - sin y - 1 = 0) for (0ᶜirc leq y leq 360ᶜirc).

a) (y = 150ᶜirc)
b) (y = 210ᶜirc)
c) (y = 30ᶜirc)
d) (y = 330ᶜirc)

Answer 1

To solve the equation (2cos² y - sin y - 1 = 0), rearrange the equation and use the quadratic formula. Substitute sin y with t and solve the quadratic equation for t. Find the value of y using sin y = t.

Step-by-step explanation:

To solve the equation (2cos² y - sin y - 1 = 0), we can use the quadratic formula. Let's rearrange the equation:

2cos² y - sin y - 1 = 0

2(1 - sin² y) - sin y - 1 = 0

2 - 2sin² y - sin y - 1 = 0

-2sin² y - sin y + 1 = 0

To solve this quadratic equation, we can substitute sin y with t. Let:

t = sin y

-2t² - t + 1 = 0

Now we can solve this quadratic equation for t. Once we find the value of t, we can find the value of y using sin y = t.

By using the quadratic formula:

t = (-b ± sqrt(b² - 4ac)) / 2a

We get two values for t, which correspond to two possible values of y. From the given options, (b) y = 210° and (d) y = 330° satisfy the original equation. Therefore, the correct answers are (b) and (d).