Chapter 9: Problem 1

Convert the following angles in radians to degrees: (a) \(0.3609\) (b) \(0.4771\) (c) \(1.3692\) (d) \(\frac{\pi}{3}\) (e) \(\frac{2 \pi}{3}\) (f) \(6 \pi\) (g) \(\frac{\pi}{5}\) (h) \(\frac{3 \pi}{2}\)

Short Answer

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Question: Convert the following angles from radians to degrees: (a) 0.3609 radians (b) 0.4771 radians (c) 1.3692 radians (d) π/3 radians (e) 2π/3 radians (f) 6π radians (g) π/5 radians (h) 3π/2 radians Answer: (a) ≈ 20.663° (b) ≈ 27.344° (c) ≈ 78.486° (d) 60° (e) 120° (f) 1080° (g) 36° (h) 270°

Step by step solution

(a) Convert 0.3609 radians to degrees

Using the conversion formula, we have: Degrees = (0.3609 × 180) ÷ π Using a calculator, find the value: Degrees ≈ 20.663°

(b) Convert 0.4771 radians to degrees

Using the conversion formula, we have: Degrees = (0.4771 × 180) ÷ π Using a calculator, find the value: Degrees ≈ 27.344°

(c) Convert 1.3692 radians to degrees

Using the conversion formula, we have: Degrees = (1.3692 × 180) ÷ π Using a calculator, find the value: Degrees ≈ 78.486°

(d) Convert π/3 radians to degrees

Using the conversion formula, we have: Degrees = (π/3 × 180) ÷ π Simplify: Degrees = 60°

(e) Convert 2π/3 radians to degrees

Using the conversion formula, we have: Degrees = (2π/3 × 180) ÷ π Simplify: Degrees = 120°

(f) Convert 6π radians to degrees

Using the conversion formula, we have: Degrees = (6π × 180) ÷ π Simplify: Degrees = 1080°

(g) Convert π/5 radians to degrees

Using the conversion formula, we have: Degrees = (π/5 × 180) ÷ π Simplify: Degrees = 36°

(h) Convert 3π/2 radians to degrees

Using the conversion formula, we have: Degrees = (3π/2 × 180) ÷ π Simplify: Degrees = 270°

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Convert the following angles in radians to degrees: (a) \(0.3609\) (b) \(0.4771\) (c) \(1.3692\) (d) \(\frac{\pi}{3}\) (e) \(\frac{2 \pi}{3}\) (f) \(6 \pi\) (g) \(\frac{\pi}{5}\) (h) \(\frac{3 \pi}{2}\)

Short Answer

Step by step solution

(a) Convert 0.3609 radians to degrees

(b) Convert 0.4771 radians to degrees

(c) Convert 1.3692 radians to degrees

(d) Convert π/3 radians to degrees

(e) Convert 2π/3 radians to degrees

(f) Convert 6π radians to degrees

(g) Convert π/5 radians to degrees

(h) Convert 3π/2 radians to degrees

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