Solve the equation for 0° ≤ x ≤ 90°. Round to the nearest degree.tan2B = 4
Question
Solve the equation for 0° ≤ x ≤ 90°. Round to the nearest degree.tan2B = 4
Solution
To solve the equation tan2B = 4 for 0° ≤ x ≤ 90°, we need to find the value of B.
Step 1: Take the inverse tangent (arctan) of both sides of the equation to isolate B.
arctan(tan2B) = arctan(4)
Step 2: Simplify the left side of the equation using the tangent double-angle identity.
2B = arctan(4)
Step 3: Divide both sides of the equation by 2 to solve for B.
B = arctan(4) / 2
Step 4: Use a calculator to find the value of arctan(4) and divide it by 2.
B ≈ 35.26°
Therefore, the solution to the equation tan2B = 4 for 0° ≤ x ≤ 90° is B ≈ 35.26°.
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