quickest way to solve for x for circular functions?

[Blondie21]

MY METHOD TAKES SO LONG! The time I take is not worth the 2 marks that these questions are normally worth.

How would you solve:
"Solve for "

This is what I do
1. Change the domain for what is in the brackets
2. Find
3. Find which quadrants this value applies to and then find the angles
4. Add and subtract 2pi from these values and find all the values that fit into the domain
5. Solve these values for x (as the values I found in step 4 are for  
6. Should have the ans by now.

This takes soooo long!! Do you all do this? Something similar? Something quicker? If so, what is it?

Thanks :-))

[lzxnl]

MY METHOD TAKES SO LONG! The time I take is not worth the 2 marks that these questions are normally worth.

How would you solve:
"Solve for "

This is what I do
1. Change the domain for what is in the brackets
2. Find
3. Find which quadrants this value applies to and then find the angles
4. Add and subtract 2pi from these values and find all the values that fit into the domain
5. Solve these values for x (as the values I found in step 4 are for  
6. Should have the ans by now.

This takes soooo long!! Do you all do this? Something similar? Something quicker? If so, what is it?

Thanks :-))

sin(2x - pi/2) = -1/2
xE [0, 2pi] so 2x-pi/2 E [-pi/2, 7pi/2]
Basic angle is -pi/6, so we have
2x - pi/2 = -pi/6 + 2n*pi and x = 7pi/6 + 2n*pi
Stay in required interval for 2x - pi/2
2x - pi/2 = -pi/6, 11pi/6 and -5pi/6, 7pi/6, 19pi/6
Solve for x and you're done