Find all angles θ between 0° and 180° satisfying the given equation. (Enter your answers as a comma-separated list. Round your answers to one decimal place.)
cos θ = 1/7
cosine is positive in QI and QIV
Find θ such that cos θ = 1/7
It is the only angle between 0° and 180° whichc has such a positive cosine value.
To find the angles θ between 0° and 180° satisfying the equation cos θ = 1/7, we can use the inverse cosine function.
Step 1: Calculate the inverse cosine of 1/7.
cos^(-1) (1/7) ≈ 80.3°
Step 2: Since the cosine function is periodic, we know that there is another angle with the same cosine value in the second quadrant. To find this angle, subtract the result from 180°.
180° - 80.3° ≈ 99.7°
So, the angles θ between 0° and 180° satisfying the equation cos θ = 1/7 are approximately 80.3° and 99.7°. Therefore, the answer is 80.3, 99.7.
To find all angles θ between 0° and 180° satisfying the equation cos θ = 1/7, we can use the inverse cosine function, also known as arccosine.
Step 1: Find the arccosine of 1/7
arccos(1/7) ≈ 81.8°
Step 2: Since cosine is a periodic function, we need to consider the other possible angles that satisfy the equation. In the range of 0° to 180°, the cosine function is positive in the first and second quadrants.
Step 3: Consider the reference angle. The reference angle is the smallest angle between the terminal side of the angle and the x-axis. To find the reference angle, we can subtract the arccosine from 180°.
Reference angle = 180° - 81.8° ≈ 98.2°
Step 4: Find the corresponding angles in the first and second quadrants.
First Quadrant: 81.8°
Second Quadrant: 180° - 81.8° ≈ 98.2°
Step 5: Round the answers to one decimal place and list them as a comma-separated list.
The angles θ that satisfy the equation cos θ = 1/7 in the range of 0° to 180° are approximately 81.8°, 98.2°.