# Small angle approximations

Loading page description...

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.

# #0

# ✅

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

# #0

# ✅

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

# #0

# ✅

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

# #0

# ✅

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

# #0

# ✅

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

# #0

# ✅

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

# #0

# ✅

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

# #0

# ✅

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

End of page