Q. Convert the angle θ=70∘ to radians.Express your answer exactly.θ=□ radians
Understanding degrees and radians: Understand the relationship between degrees and radians.One complete revolution is 360∘, which is equivalent to 2π radians. Therefore, to convert degrees to radians, we use the conversion factor 180∘π radians.
Setting up the conversion: Set up the conversion for 70 degrees to radians using the relationship from Step 1.θ in radians=θ in degrees×(180 degreesπ radians)
Substituting values: Substitute 70 for θ in degrees into the conversion formula.θ in radians = 70×(180π)
Simplifying the expression: Simplify the expression by multiplying 70 by π and then dividing by 180.θ in radians = (70π)/180
Reducing the fraction: Reduce the fraction(70π)/180 to its simplest form.Both 70 and 180 are divisible by 10, so we can simplify the fraction by dividing both the numerator and the denominator by 10.θ in radians = (7π)/18
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