Radians quiz #1 Flashcards
Radians quiz #1
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What is 270 degrees converted to radians? 270 degrees is (3π/2) radians. How many radians is 342 degrees? 342 degrees is (342 × π) / 180 = (171π/90) radians. Which radian measure is equal to a given degree measure? To convert degrees to radians, multiply the degree measure by π/180. How many radians is 216 degrees? 216 degrees is (216 × π) / 180 = (6π/5) radians. How many radians are in a full circle? A full circle is 2π radians. What is the radian equivalent for 180 degrees? 180 degrees is π radians. How many radians is 200 degrees? 200 degrees is (200 × π) / 180 = (10π/9) radians. How do you locate the position of 7 radians on the number line? To locate 7 radians, mark a point at 7 units from the origin on the radian number line. How many radians are in half of a circle? Half of a circle is π radians. How many radians are in a quarter of a circle? A quarter of a circle is (π/2) radians. How many radians are in 27 degrees? 27 degrees is (27 × π) / 180 = (3π/20) radians. How many radians is 105 degrees? 105 degrees is (105 × π) / 180 = (7π/12) radians. How many radians is 340 degrees? 340 degrees is (340 × π) / 180 = (17π/9) radians. If an angle measures 4.3 radians, what is its measure in degrees to the nearest degree? 4.3 radians is approximately 4.3 × (180/π) ≈ 246 degrees. How many radians is -135 degrees? -135 degrees is (-135 × π) / 180 = (-3π/4) radians. What is the formula for the area of a sector given a central angle in radians and a radius r? The area of a sector is (1/2) × r² × θ, where θ is in radians. How many radians is 180 degrees? 180 degrees is π radians. Which expression converts 45 degrees to radians? 45 degrees × (π/180) = (π/4) radians. What is 720 degrees converted to radians? 720 degrees is (720 × π) / 180 = 4π radians. What is the formula for the area of a sector given a central angle in radians? The area of a sector is (1/2) × r² × θ, where θ is in radians. How many radians is 150 degrees? 150 degrees is (150 × π) / 180 = (5π/6) radians. How do you express the radian measure of a central angle given in degrees? Multiply the degree measure by π/180 to convert to radians. How many degrees is 2π/9 radians? 2π/9 radians is (2π/9) × (180/π) = 40 degrees. If an arc is a fraction f of the circumference of a circle, what is the radian measure of the central angle? The radian measure is 2π × f, where f is the fraction of the circumference. How many radians of angle are covered in one full revolution in circular motion? One full revolution covers 2π radians. What is the formula for the area of a sector given a central angle in radians and a radius r? The area of a sector is (1/2) × r² × θ, where θ is in radians. If an arc on a circle measures 250 degrees, within which range is the radian measure of the central angle? 250 degrees is between (4π/3) and (3π/2) radians. If an arc is a fraction f of the circumference of a circle, what is the radian measure of the central angle? The radian measure is 2π × f, where f is the fraction of the circumference. What is the total radian measure of the angle the minute hand travels in 4 full rotations? 4 full rotations is 4 × 2π = 8π radians. What is the formula for the length of an arc given the radius r and central angle θ in radians? Arc length = r × θ, where θ is in radians. How many degrees is negative π/8 radians? Negative π/8 radians is (-π/8) × (180/π) = -22.5 degrees. How many radians is 280 degrees? 280 degrees is (280 × π) / 180 = (14π/9) radians. How many degrees is 17π/10 radians? 17π/10 radians is (17π/10) × (180/π) = 306 degrees. How do you convert an angle in radians to degrees? Multiply the radian measure by 180/π to convert to degrees. How do you express the radian measure of a central angle given in degrees? Multiply the degree measure by π/180 to convert to radians. How do you find all exact solutions to an equation involving trigonometric functions in radians? List all solutions in the form θ = solution + 2πk, where k is any integer. How many degrees is negative π/8 radians? Negative π/8 radians is -22.5 degrees. How many degrees is 7π/10 radians? 7π/10 radians is (7π/10) × (180/π) = 126 degrees. How many radians is 126 degrees? 126 degrees is (126 × π) / 180 = (7π/10) radians. How do you determine the radian measure of an angle given its degree measure? Multiply the degree measure by π/180 to convert to radians.
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