This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
here are the solutions to the trigonometry questions: 1. What is ()/(3) rad in degrees? Step 1: To convert radians to degrees, use the conversion factor (180^)/( rad). Degrees = Radians × (180^)/() Step 2: Substitute the given radian value into the formula. Degrees = ()/(3) × (180^)/() Step 3: Cancel out and perform the multiplication. Degrees = (180^)/(3) = 60^ The correct option is C. C. 60^ 2. Determine the length of an arc which subtends an angle of 0.8 rad at the centre of a circle of radius 10 cm. Step 1: The formula for the length of an arc (s) is s = r, where r is the radius and is the angle in radians. Given: r = 10 cm, = 0.8 rad. Step 2: Substitute the given values into the formula. s = (10 cm) × (0.8 rad) Step 3: Calculate the arc length. s = 8 cm The correct option is B. B. 8 cm 3. Calculate the area of a sector containing an angle of 1.5 rad, in a circle of radius 2 cm. Step 1: The formula for the area of a sector (A) is A = (1)/(2)r^2, where r is the radius and is the angle in radians. Given: r = 2 cm, = 1.5 rad. Step 2: Substitute the given values into the formula. A = (1)/(2) (2 cm)^2 (1.5 rad) Step 3: Calculate the square of the radius. A = (1)/(2) (4 cm^2) (1.5) Step 4: Perform the multiplication. A = 2 cm^2 × 1.5 A = 3 cm^2 The correct option is A. A. 3 cm^2 Drop the next question!