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Convert the angle 
theta=70^(@) to radians.
Express your answer exactly.

theta=◻"-x radians "

Convert the angle θ=70 \theta=70^{\circ} to radians.\newlineExpress your answer exactly.\newlineθ= radians  \theta=\square \text { radians }

Full solution

Q. Convert the angle θ=70 \theta=70^{\circ} to radians.\newlineExpress your answer exactly.\newlineθ= radians  \theta=\square \text { radians }
  1. Understanding degrees and radians: Understand the relationship between degrees and radians.\newlineOne complete revolution is 360360^\circ, which is equivalent to 2π2\pi radians. Therefore, to convert degrees to radians, we use the conversion factor π radians180\frac{\pi \text{ radians}}{180^\circ}.
  2. Setting up the conversion: Set up the conversion for 7070 degrees to radians using the relationship from Step 11.\newlineθ in radians=θ in degrees×(π radians180 degrees)\theta \text{ in radians} = \theta \text{ in degrees} \times \left(\frac{\pi \text{ radians}}{180 \text{ degrees}}\right)
  3. Substituting values: Substitute 7070 for θ\theta in degrees into the conversion formula.\newlineθ\theta in radians = 70×(π180)70 \times \left(\frac{\pi}{180}\right)
  4. Simplifying the expression: Simplify the expression by multiplying 7070 by π\pi and then dividing by 180180.\newlineθ\theta in radians = (70π)/180(70\pi) / 180
  5. Reducing the fraction: Reduce the fraction (70π)/180(70\pi) / 180 to its simplest form.\newlineBoth 7070 and 180180 are divisible by 1010, so we can simplify the fraction by dividing both the numerator and the denominator by 1010.\newlineθ\theta in radians = (7π)/18(7\pi) / 18

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