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).7, cosine, A, minus, 2, equals, cosine, A, plus, 47cosA−2=cosA+4

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).7, cosine, A, minus, 2, equals, cosine, A, plus, 47cosA−2=cosA+4

🧐 Not the exact question you are looking for?Go ask a question

Solution 1

The given equation is 7cosA - 2 = cosA + 4.

First, let's simplify this equation by subtracting cosA from both sides:

7cosA - cosA = 2 + 4

This simplifies to:

6cosA = 6

Next, divide both sides by 6:

cosA = 1

The cosine function equals 1 at two points in the interval 0 ≤ A < 360: at 0 degrees and 360 degrees. However, since 360 degrees is not included in the interval, the only solution in this interval is A = 0 degrees.

This problem has been solved

Solution 2

The given equation is cosA - 2 = cosA + 4.

Step 1: Subtract cosA from both sides of the equation to isolate the constants. This gives us -2 - cosA = 4.

Step 2: Simplify the equation by multiplying through by -1. This gives us 2 + cosA = -4.

Step 3: Subtract 2 from both sides of the equation to isolate cosA. This gives us cosA = -6.

However, the range of the cosine function is -1 ≤ cosA ≤ 1. Therefore, there are no angles A that satisfy the equation cosA = -6.

This problem has been solved

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, theta, is less than, 360, degrees, comma0 ∘ ≤θ<360 ∘ , that satisfy the equation below, to the nearest tenth of a degree.cosine, left parenthesis, theta, right parenthesis, equals, one quartercos(θ)= 41

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, theta, is less than, 360, degrees0 ∘ ≤θ<360 ∘ , that satisfy the equation below, to the nearest tenth of a degree (if necessary).minus, tangent, theta, plus, 2, equals, 4, tangent, theta, plus, 7−tanθ+2=4tanθ+7

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

1/3

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.