Question

Find all angles, 0, degrees, is less than or equal to, C, is less than, 360, degrees0 ∘ ≤C<360 ∘ , that satisfy the equation below, to the nearest tenth of a degree (if necessary). 6, cosine, C, minus, 3, equals, cosine, C, minus, 6 6cosC−3= cosC−6

Answer 1

To find the angles that satisfy the equation 6cosC − 3 = cosC − 6, we solve for cosC and use the inverse cosine function to determine the two angles between 0 and 360 degrees. Adjust the angles to the nearest tenth and ensure the use of degrees in calculations.

Step-by-step explanation:

The question requires finding angles between 0 degrees and 360 degrees that satisfy the equation 6cosC − 3 = cosC − 6. To solve this, we can rearrange the equation to isolate cosC:

1. Move all terms containing cosC to one side: 6cosC − cosC = − 6 + 3.
2. Simplify: 5cosC = − 3.
3. Divide by 5: cosC = − 3/5.
4. Use the inverse cosine function: C = cos−¹ (− 3/5).

Using a calculator, we obtain two solutions between 0 and 360 degrees because the cosine function is positive in the first and fourth quadrants and negative in the second and third quadrants. To find these angles we calculate the primary angle and then use the symmetry of the cosine function to find the secondary angle.

After finding the principal angle, you would calculate 180 degrees − principal angle and 180 degrees + principal angle to determine the angles in the second and third quadrants respectively. Remember to adjust the angle to the closest tenth if necessary and make sure your calculator is set to degrees mode.