Question

30. If 8 sin^2 θ + 2 sin θ − 1 = 0, then what is the smallest
positive value of θ?
(A) 7.3°
(B) 14.5°
(C) 30°
(D) 60°
(E) 75.5°

What are the steps to get the answer?

Answer 1

that's same as quadratic equation Ax^2+Bx+C=0
let sin theta =y
you can rewrite it as \[\huge\rm 8y^2+ 2 y − 1 = 0\]
can you find factor of this equation ?

Answer 2

y^2 + 2y - 8 = 0
(y+4)(y-2)=0
y = -4, 2

Answer 3

So, how do I figure out the degrees?

Answer 4

hmm you can't just move the leading to constant term
...

Answer 5

you need to multiply AC but that doesn't mean you can write 8 as the constant term.

Answer 6

AC= leading coefficient times constant term
so 8 times -1=-8 now find two numbers whose product equal to AC
and sum should be equal to coefficient of y term

Answer 7

So AC = -8
Sum = 2

+4, -2

Answer 8

correct now since the leading coefficient isn't one try group by factoring method
keep the first and constant term and write both numbers in the middle by factor by grouping