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Question Video: Solving Trigonometric Equations Using the Trigonometric Values of Special Angles Mathematics • 10th Grade

Given that sin 60° cos 30° − cos 60° sin 30° = sin 𝜃°, find the value of 𝜃, given that the angle is acute.

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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.

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