Find, to the nearest tenth of a degree, all positive angles less than 360° where cos θ = -0.5982
they will be in QII and QIII.
cos 53.3° = 0.5982
Use that for your reference angle.
To find all the positive angles less than 360° where cos θ = -0.5982, we can use the inverse cosine function (also known as arccosine).
Step 1: Use the inverse cosine function on the given value of cos θ.
arccos(-0.5982)
Step 2: Evaluate the inverse cosine using a calculator or a table of trigonometric functions.
arccos(-0.5982) ≈ 128.036°
Step 3: Since the cosine function has a periodicity of 360°, we need to find all positive angles that differ by a multiple of 360° from the initial angle.
For example, 128.036° + 360° = 488.036°
And 128.036° - 360° = -231.964° (negative angle)
Step 4: Since we are looking for positive angles less than 360°, we exclude any angle greater than 360° or negative angles.
Therefore, the positive angles less than 360° where cos θ = -0.5982, to the nearest tenth of a degree, are:
128.0° and 231.9°.