Find all angles, 0, degrees, is less than or equal to, A, is less than, 360, degrees0 ∘ ≤A<360 ∘ , that satisfy the equation below, to the nearest tenth of a degree (if necessary).4, sine, A, plus, 4, equals, 2, sine, A, plus, 54sinA+4=2sinA+5
Question
Find all angles, 0, degrees, is less than or equal to, A, is less than, 360, degrees0 ∘ ≤A<360 ∘ , that satisfy the equation below, to the nearest tenth of a degree (if necessary).4, sine, A, plus, 4, equals, 2, sine, A, plus, 54sinA+4=2sinA+5
Solution
The given equation is 4sinA + 4 = 2sinA + 5.
Step 1: Subtract 2sinA from both sides to get 2sinA + 4 = 5.
Step 2: Subtract 4 from both sides to get 2sinA = 1.
Step 3: Divide both sides by 2 to get sinA = 0.5.
Now we need to find all angles A such that 0 ≤ A < 360 and sinA = 0.5.
The sine function has a value of 0.5 at two points within a 360 degree cycle: 30 degrees and 150 degrees (in the first and second quadrants respectively, where sine is positive).
So, the solutions to the equation are A = 30 degrees and A = 150 degrees.
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