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The following are all angle measures (in degrees, rounded to the nearest tenth) whose sine is 0.36 . Which is the principal value of arcsin(0.36) ? Choose 1 answer: (A) 21.1^(@) (B) 381.1^(@) (c) 741.1^(@) (D) 1101.1^(@)

The following are all angle measures (in degrees, rounded to the nearest tenth) whose sine is 00.3636 .\newlineWhich is the principal value of arcsin⁡(0.36) \arcsin (0.36) ?\newlineChoose 11 answer:\newline(A) 21.1∘ 21.1^{\circ} \newline(B) 381.1∘ 381.1^{\circ} \newline(C) 741.1∘ 741.1^{\circ} \newline(D) 1101.1∘ 1101.1^{\circ}

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Q. The following are all angle measures (in degrees, rounded to the nearest tenth) whose sine is 00.3636 .\newlineWhich is the principal value of arcsin⁡(0.36) \arcsin (0.36) ?\newlineChoose 11 answer:\newline(A) 21.1∘ 21.1^{\circ} \newline(B) 381.1∘ 381.1^{\circ} \newline(C) 741.1∘ 741.1^{\circ} \newline(D) 1101.1∘ 1101.1^{\circ}
  1. Understand principal value concept: Understand the concept of the principal value for the arcsine function.\newlineThe principal value of arcsin⁡(x)\arcsin(x) is the value of the angle in the range from −90∘-90^\circ to 90∘90^\circ whose sine is xx. Since 0.360.36 is positive, the principal value will be in the first quadrant, between 0∘0^\circ and 90∘90^\circ.
  2. Use calculator for arcsin⁡(0.36)\arcsin(0.36): Use a calculator to find the principal value of arcsin⁡(0.36)\arcsin(0.36). By inputting the value into a calculator, we can find the principal value of arcsin⁡(0.36)\arcsin(0.36). Make sure the calculator is set to degree mode.
  3. Verify calculator's result: Verify the calculator's result.\newlineAfter calculating, we find that the principal value of arcsin⁡(0.36)\arcsin(0.36) is approximately 21.121.1 degrees. This is within the expected range for the principal value.
  4. Compare with given options: Compare the result with the given options.\newlineThe calculated value of approximately 21.121.1 degrees matches option (A)(A). Options (B)(B), (C)(C), and (D)(D) are not within the range of −90∘-90^\circ to 90∘90^\circ, so they cannot be principal values of arcsin⁡(0.36)\arcsin(0.36).

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