Find all values of \(\theta\) between 0 and 360 degrees that satisfy \(\cos(\theta) = -0.73\).

cos θ = − 0.73 − cos θ = 0.73 cos ( 18 0 o − θ ) = 0.73 or cos ( 18 0 o + θ ) = 0.73 18 0 o − θ = 4 3 o or 18 0 o + θ = 4 3 o θ = 13 7 o or θ = − 13 7 o → θ = − 13 7 o + 36 0 o = 22 3 o A n s w er : θ = 13 7 o or θ = 22 3 o

Answered by Anonymous | 2024-06-10

The values of θ that satisfy cos ( θ ) = − 0.73 in the range of 0° to 360° are approximately 137.58° and 223.58°. These angles fall in the second and third quadrants where the cosine function is negative. Calculating the reference angle and adjusting for the appropriate quadrants leads to the solutions.
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Answered by Anonymous | 2024-12-23