Solve sin x= 1/2 on the interval without using a calculator [0,2π).

Question

Any extra details of explanation will be appreciated to understand. Thank u.

Answer 1

30-60 right triangles and 45-45 right triangles are so common and fundamental in trigonometry (and calculus, etc) that you will save a lot of time in the long run by memorizing these special angles and their trig function values, on the Unit Circle. Draw a unit circle (radius = 1), and then label these angles and their basic trig values.

Degrees Radians Cosine Sine

0 0 1 0

30 π / 6 √3 / 2 1 / 2 √3 / 2 is about .866

45 π / 4 √2 / 2 √2 / 2 √2 / 2 is about .707

60 π / 3 1 / 2 √3 / 2

90 π / 2 0 1

Answer 2

arcsin 0.5 = 30° This from the 30-60-90 triangle.

Sine is also positive in QII.

arcsin 0.5 = 30º and 150º