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Find all angles, 0^(@) <= theta < 360^(@), that solve the following equation. sin theta=1 Answer: theta=

Find all angles, 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} , that solve the following equation.\newlinesin⁡θ=1 \sin \theta=1 \newlineAnswer: θ= \theta=

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Q. Find all angles, 0∘≤θ<360∘ 0^{\circ} \leq \theta<360^{\circ} , that solve the following equation.\newlinesin⁡θ=1 \sin \theta=1 \newlineAnswer: θ= \theta=
  1. Identify Maximum Sine Angle: Identify the angle where the value of sine is 11. The sine function reaches its maximum value of 11 at an angle where the point on the unit circle is at the highest point above the x-axis. This occurs at θ=90\theta = 90 degrees or θ=π2\theta = \frac{\pi}{2} radians.
  2. Check for Additional Angles: Determine if there are any other angles within the given range that also have a sine value of 11. Since the sine function is periodic with a period of 360360 degrees or 2π2\pi radians, we look for other angles that are coterminal with 9090 degrees. However, within the range of 00 to 360360 degrees, the sine function only reaches the value of 11 once, at θ=90\theta = 90 degrees.
  3. List Satisfying Angles: List all the angles that satisfy the equation within the given range.\newlineThe only angle between 00 degrees and 360360 degrees where sin⁡(θ)=1\sin(\theta) = 1 is at θ=90\theta = 90 degrees.

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