Home
Class 12
MATHS
A circular ring of radius 3cm hangs hori...

A circular ring of radius 3cm hangs horizontally form a point 4cm vertically above the centre by 4 strings attached at equal intervals to its circumference. If the angle between two consecutive strings be `theta` , then `costheta` is equal to `4/5` (b) `4/(25)` (d) `(16)/(25)` (d) none of these

Text Solution

Verified by Experts

Let P be the point from which the ring is hanging .Also ,let the strings are attached to the point A,B,C and D at the ring .

In the figure ,
OP =4
OA =OB=OC=OD=3
AP = BP =CP =DP `=sqrt(3^2+4^2)=5`
ABCD is square of sides lenght `3sqrt(2)` cm Now in triangle PDB.
`sin""(theta)/2=(1/2 BC)/(BP)=(3/sqrt(2))/5=(3)/(5sqrt(2))`
`therefore cos theta = 1-2 sin ^2""(theta)/(2)=16/25`
Promotional Banner

Topper's Solved these Questions

  • HIGHT AND DISTANCE

    CENGAGE ENGLISH|Exercise Exercises|18 Videos

  • HIGHT AND DISTANCE

    CENGAGE ENGLISH|Exercise Archives|3 Videos

  • GRAPHS OF TRIGONOMETRIC FUNCTIONS

    CENGAGE ENGLISH|Exercise Exercises|22 Videos

  • HYPERBOLA

    CENGAGE ENGLISH|Exercise COMPREHENSION TYPE|2 Videos

Similar Questions

Explore conceptually related problems

A circular ring of radius 3cm hangs horizontally from a point 4 cm vertically above the centre by 4 strings attached at equal intervals to its circumference. If the angle between two consecutive strings be theta , then costheta is equal to (A) 4/5 (B) 4/(25) (C) (16)/(25) (D) none of these

A circular ring of radius 5 cm is suspended horizontally from a point 12 cm vertically above its centre by 6 strings attached to its circumference at equal intervals. The cosine of the angle between two consecutive ring is

A ring,10 cm in diameter, is suspended from a point 12cm above its centre by 6 equal strings attached to its circumference at equal intervals. Find the cosine of the angle between consecutive strings.

2(sin^6theta+cos^6theta)-3(sin^4theta+cos^4theta) is equal to 0 (b) 1 (c) -1 (d) None of these

If tantheta=3/4 , then cos^2theta-sin^2theta= (a) 7/(25) (b) 1 (c) -7/(25) (d) 4/(25)

2(sin^6theta+cos^6theta)-3(sin^4theta+cos^4theta) is equal to (a) 0 (b) 1 (c) -1 (d) None of these

Two circles of radii 4cm and 1cm touch each other externally and theta is the angle contained by their direct common tangents. Then sintheta is equal to (a) (24)/(25) (b) (12)/(25) (c) 3/4 (d) none of these

If costheta=2/3 , then 2sec^2theta+2tan^2theta-7 is equal to (a) 1 (b) 0 (c) 3 (d) 4

If theta is the angle between any two vectors vec a and vec b , then vec a. vec b=| vec axx vec b| when theta is equal to (a) 0 (B) pi/4 (C) pi/2 (d) pi

The number of solution of the equation sin2theta-2costheta+4sintheta=4in[0,5pi] is equal to 3 (b) 4 (c) 5 (d) 6