Video Transcript
Given that sin 60 degrees times cos
30 degrees minus cos 60 degrees times sin 30 degrees equals sin 𝜃, find the value
of 𝜃, given that the angle is acute.
When we look at this equation, we
notice that we’re dealing with angles of 60 degrees and 30 degrees. And if we replace them with 𝐴 and
𝐵, it should remind us of this trigonometric difference identity. sin of angle 𝐴 minus angle 𝐵 is
equal to sin of angle 𝐴 times cos of angle 𝐵 minus cos of angle 𝐴 times sin of
angle 𝐵. So if we use 𝐴 equals 60 and 𝐵
equals 30, we see that 𝐴 degrees minus 𝐵 degrees is 60 degrees minus 30 degrees,
which is of course 30 degrees. This means then that 𝜃 is equal to
30.
Now, remember that the question
told us that the angle is acute. So we’re only looking for values of
𝜃 between zero and 90. Now, sin of 30 is 0.5, or a
half. And in that interval from zero to
90, there’s only one value of 𝜃 which gives an answer of sin 𝜃 is equal to 0.5,
and that is 30. So the answer is that the value of
𝜃 is 30.
