Tamil Nadu Board Solutions for Chapter: Trigonometry, Exercise 2: Exercise

In a circle of diameter $40$ cm, a chord is of length $20$ cm. Find the length of the minor arc of the chord. [Enter the value without units correct to two decimal places and take $\mathrm{\pi }=\frac{22}{7}$].

Find the degree measure of the angle subtended at the center of the circle of the radius $100 \mathrm{cm}$by an arc of length $22 \mathrm{cm}$.

What is the length of the arc intercepted by a central angle of measure $41°$ in a circle of radius $10\mathrm{ft}$? [Write the answer without units correct to two decimal places and take $\mathrm{\pi }=\frac{22}{7}$]

If in two circles, arcs of the same length subtend angles $60°$ and $75°$ at the centre, find the ratio of their radii.  [Write the answer in fraction]

The perimeter of a certain sector of a circle is equal to the length of the arc of a semi-circle having the same radius. Express the angle of the sector in degrees, minutes and seconds.

An airplane propeller rotates $1000$ times per minute. Find the number of degrees that a point on the edge of the propeller will rotate in $1$ second.

A train is moving on a circular track of $1500$ m radius at the rate of $66$ km/hr. What angle will it turn in $20$ seconds? (Write the answer without degree symbol)

A circular metallic plate of radius $8$ cm and thickness $6$ mm is melted and molded into a pie (a sector of the circle with thickness) of radius $16$ cm and thickness $4$ mm. If the angle of the sector is $\frac{k\pi }{4}$ radians. Find the value of $k$.