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14 Cards in this Set
- Front
- Back
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Radian meassure of an angle is ____________________.
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Radian measure of an angle is the length of the arc on the unit subtended by the angle.
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Convert the radian meausre n/4 to degrees.
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(n/4)(18/n)=180/4=45 degrees
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How long is the arc subtended by an angle of 5n/2 radians on a circle of radius 30 cm?
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sθr=5n/2(30) = 75n≈235.5cm
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Let sin θ=6/16. Find the value of cos θ=using unit the circle.
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cos θ= cos(x)= sin(n/2-x)= 55/4
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Let sin θ=6/16. Find the value of tan θ using the unit circle.
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tan θ=sin θ/cos θ θ=3/110
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Let sin θ=6/16. Find the value of sec θ using the unit circle.
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sec θ=1/cos θ=4/55
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Let sin θ=6/16. Find the value of csc θ using the unit circle.
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csc θ=1/sin θ=8/3
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Find the value of sin(-π/3)
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The sine function f(t)=sin t is odd and the cosine function g(t)= cos t is even; that is, for every real number t, sin (-π/3)= -sin(π/3) = -√3/2 cos (-π/3)=cosπ/3= 1/2. Note that the signs of the answers are consistent with the fact that the terminal side of the angle -π/3 radian lies in quadrant IV
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Find the value of sin(-2π/3)
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The sine function f(t)=sin t is odd and the cosine function g(t)= cos t is even; that is, for every real number t, sin (-2π/3)= -sin(2π/3) = -√3/2 cos (-2π/3)= cos2π/3= -1/2 Note that the signs of the answers are consistent with the fact that the terminal side of the angle -2π/3 radian lies in quadrant III
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Find the exact value of sin(-3π/4)
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The sine function f(t)=sin t is odd and the cosine function g(t)= cos t is even; that is, for every real number t, sin (-3π/4)= -sin(3π/4) = -√2/2 cos (-3π/4)= cos3π/4= -√2/2. Note that the signs of the answers are consistent with the fact that the terminal side of the angle -3π/4 radian lies in quadrant III.
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What is the value of h in this diagram?
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h=12√3
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convert 180° to radians using the unit circle.
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120° (π/180)=2π/3 radians
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Convert π/5 into degrees using the unit circle.
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π/5(180/π)=180/5=36°
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According to the unit circle, is the sine function odd or even?
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The sine is an odd function because f(-x)=-f(x) for all x values in the domain of f.
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