Find the measure of the reference angle for an 11 radian radian angle.

Mathematics

1 answer:

Vesnalui [34]2 years ago

4 0

Answer:

about 1.56637 radians ≈ 89.746°

Step-by-step explanation:

The reference angle in radians can be found by the formula ...

ref angle = min(mod(θ, π), π -mod(θ, π))

Equivalently, it is ...

ref angle = min(ceiling(θ/π) -θ/π, θ/π -floor(θ/π))×π

<h3>Application</h3>

When we divide 11 radians by π, the result is about 3.501409. The fractional part of this quotient is more than 1/2, so the reference angle will be ...

ref angle = (1 -0.501409)π radians ≈ 1.56637 radians ≈ 89.746°

Additional comment

For calculations such as this, you need to use the most accurate value of pi available. The approximations 22/7 or 3.14 are not sufficiently accurate to give good results.

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