Question

If theta is a positive acute angle find theta when
6 sin^2 theta - 11 sin theta + 4=0​

Answer 1

Theta = 30 degrees

Explanation:

6 sin^2 theta - 11 sin theta + 4=0​

First we factorise the expression:

Note: product of the first and last coefficients = 6 * 4 = 24.

So we need 2 numbers whose product is 24 and whose sum = the second coefficient (-11).

These numbers are -3 and -8, so we write the original equation as:

6 sin^2 theta - 3sin theta - 8 sin theta + 4 = 0​

Now we factorise by grouping:

3 sin theta(2 sin theta - 1) - 4 (2 sin theta - 1) = 0

2 sin theta - 1 is common so we have:

(2 sin theta - 1)(3 sin theta - 4) = 0

So sin theta = 1/2 or sin theta = 1.3333

This gives theta = 30 degrees ( as 1.3333 is invalid for a sine).