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Rotate the yellow dot to a location of 4 radians. After you rotate the angle, determine the value of sec 4, to the nearest hundredth.

Rotate the yellow dot to a location of 44 radians. After you rotate the angle, determine the value of sec⁡4 \sec 4 , to the nearest hundredth.

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Full solution

Q. Rotate the yellow dot to a location of 44 radians. After you rotate the angle, determine the value of sec⁡4 \sec 4 , to the nearest hundredth.
  1. Understand sec⁡θ\sec \theta Reciprocal: To solve for sec⁡4\sec 4, we first need to understand that sec⁡θ\sec \theta is the reciprocal of cos⁡θ\cos \theta. Therefore, sec⁡4\sec 4 is equal to 1cos⁡4\frac{1}{\cos 4}.
  2. Calculate Cos 44 Radians: We need to find the value of cos⁡4\cos 4. Since our calculators are typically in degree mode, we need to ensure that we are calculating the cosine of 44 radians, not 44 degrees.
  3. Find cos⁡4\cos 4 Value: Using a calculator set to radian mode, we find the value of cos⁡4\cos 4. The cosine of 44 radians is approximately −0.65364362-0.65364362.
  4. Calculate Sec 44: Now, we take the reciprocal of cos⁡4\cos 4 to find sec⁡4\sec 4. So, sec⁡4\sec 4 is equal to 1(−0.65364362)\frac{1}{(-0.65364362)}.
  5. Reciprocal Calculation: Calculating the reciprocal, we get sec⁡4≈−1.53073373\sec 4 \approx -1.53073373.
  6. Round to Nearest Hundredth: Finally, we round sec⁡4\sec 4 to the nearest hundredth, which gives us sec⁡4≈−1.53\sec 4 \approx -1.53.

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