Find all angles, 0, degrees, is less than or equal to, B, is less than, 360, degrees0 ∘ ≤B<360 ∘ , that satisfy the equation below, to the nearest tenth of a degree (if necessary).minus, tangent, B, minus, 5, equals, tangent, B, minus, 4−tanB−5=tanB−4
Question
Find all angles, 0, degrees, is less than or equal to, B, is less than, 360, degrees0 ∘ ≤B<360 ∘ , that satisfy the equation below, to the nearest tenth of a degree (if necessary).minus, tangent, B, minus, 5, equals, tangent, B, minus, 4−tanB−5=tanB−4
Solution
The given equation is -tanB - 5 = tanB - 4.
Step 1: Combine like terms.
This gives us 2tanB = 1.
Step 2: Solve for B.
Divide both sides by 2 to isolate tanB. This gives us tanB = 1/2.
Step 3: Find the angle B.
Use the inverse tangent function to find the angle. B = arctan(1/2).
Step 4: Convert to degrees.
B = arctan(1/2) * (180/π) ≈ 26.6 degrees.
Step 5: Find all angles between 0 and 360 degrees.
The tangent function has a period of 180 degrees, so we add 180 to our initial solution to find the next solution in the specified range.
B = 26.6 + 180 = 206.6 degrees.
So, the angles that satisfy the equation are B = 26.6 degrees and B = 206.6 degrees.
Similar Questions
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
Find all angles, 0, degrees, is less than or equal to, B, is less than, 360, degrees0 ∘ ≤B<360 ∘ , that satisfy the equation below, to the nearest tenth of a degree (if necessary).12, cosine, B, plus, 2, equals, 4, cosine, B, plus, 112cosB+2=4cosB+1
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).2, tangent, A, plus, 14, equals, 5, tangent, A, plus, 82tanA+14=5tanA+8
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).6, tangent, A, plus, 6, equals, 3, tangent, A, plus, 46tanA+6=3tanA+4
Find all angles, 0, degrees, is less than or equal to, B, is less than, 360, degrees0 ∘ ≤B<360 ∘ , that satisfy the equation below, to the nearest tenth of a degree (if necessary).7, sine, B, minus, square root of, 30, end square root, equals, 07sinB− 30 =0
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.