Small angle approximations

Like degrees, radians are an alternative unit for measuring angle. There are 360º, or 2π radians in a full turn.

The small-angle approximations are estimates of the basic trigonometric functions, valid when θ ≈ 0 and θ is in radians.

We can use the small-angle approximations to solve more complicated algebraic expressions.

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How many degrees are there in 2/3π radians?

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State the value of y.

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Give the small-angle approximation for sinθ.

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Give the small-angle approximation for tanθ.

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Give the small-angle approximation for cosθ.

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We can use the small-angle approximation for cosine when the hypotenuse is approximately equal in length to the ... side.

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Use the small-angle approximations to estimate the value of sinθ/tanθ.

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Use the small-angle approximations to estimate the value of cosθ/sinθ.

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Use the small-angle approximations to estimate the value of tanθ/cosθ.

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Using the small-angle approximations, sinθ/cosθ × A = θ. What trigonometric function is A?

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Given that θ is small and is measured in radians, use the small angle approximations to find the approximate value of (1 − cos4θ)/(2θsin3θ).

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Approximate, when x is small, (cos(3x) − 1)/(xsin(4x)).

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Given that θ is small and is measured in radians, prove that 6θ × tan(3θ)/(1 − cos(6θ)) = 1.

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Given that θ is small and is measured in radians, simplify (1 − cos3θ)/(1 − cosθ).

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Given that θ is small and is measured in radians, find (1 − cosθ)(sin3θ)/(tan6θ).

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Given that θ is small and is measured in radians, simplify (tan3θ)(sin2θ)/4θ.

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Given that θ is small and is measured in radians, find (2θtanθ)/sin6θ.

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Given that θ is small and is measured in radians, simplify [(1 − cos2θ) − tan2θ]/θ.

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State the value of x.

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Convert 180º to radians.

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Convert π/2 radians to degrees.

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How many radians are in 60º?

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How many radians are in the angle at the centre of half a circle?

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How many degrees are there in 3π radians?

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