Natasha Awada, Paul La Rondie, Laurie Buchanan and, Jill Stevens Solutions for Chapter: Periodic Relationships: Trigonometric Functions, Exercise 8: Exercise 12B

Find the area of the sector in below circle.

Find the area of the sector in below circle.

The sector formed by a central angle of $\frac{\pi }{12}$ has an area of $3\pi {\mathrm{cm}}^2$. Find the radius of the circle.

A sector has a radius of $12 \mathrm{m}$ and area of $36\mathrm{\pi } {\mathrm{m}}^2$. Find the central angle which forms the sector is of the form of $\frac{\mathrm{\pi }}{a}$, then $a=$

A sector has a radius of $12 \mathrm{m}$ and area of $36\mathrm{\pi } {\mathrm{m}}^2$. Find the the perimeter of the sector.

Find the shaded area when $\theta =1.5$ rad.

The pendulum on a large grandfather clock swings from one side to the other once every second. The length of the pendulum is $4 \mathrm{m}$ and the angle through which it swings is $\frac{\pi }{12}$. Find the total distance the tip of the pendulum travels in one minute.

A complete turn has $360$ degrees, and each degree is divided into $60$ parts called minutes.

When the central angle with its vertex at the centre of the earth has a measure of $1$ minute, the arc on the surface of the earth that is formed by this angle (known as the great-circle distance) has a measure of $1$ nautical mile.

The radius of the earth is approximately $6371 \mathrm{km}$. Find how many $\mathrm{km}$ there are in $1$ nautical mile.