Question

solve the equation on the interval 0≤x≤2pi

sinx=√(3)/2

Answer 1

For what angle is the sine graph sqrt(3) / 2? From special angles we know that sin(pi / 3) = sqrt(3) / 2

But we also know that the sine graph hits this point twice. Using the Cast rule, we know that sine is positive in the first and second quadrants. This gives us pi / 3 and 2pi / 3 as solutions.

So x = pi/3, 2pi/3

Answer 2

@erin512

Answer 3

thank you soo much @genius12
do you know how to solve this one for the same type of problem?
cosx=-1/2

Answer 4

Do you know when cosine is 1/2? Cosine graph hits 1/2 when the angle is pi/3. But here we have to find when it hits -1/2. But we know that it hits 1/2 at pi/3, so to find when it hits -1/2, we use Cast rule. We know cosine is negative in the second and third quadrant. This means that cos(x) = -1/2 at x = 2pi/3, 4pi/3

@erin512

Answer 5

thank you soo much! could you possibly help me with one more problem like this? i'll repost it now so i can give you best answer again @genius12