Advertisements
Advertisements
प्रश्न
State whether the statement is True or False? Also give justification.
One value of θ which satisfies the equation sin4θ - 2sin2θ - 1 lies between 0 and 2π.
पर्याय
True
False
Advertisements
उत्तर
This statement is False.
Explanation:
Given equation is sin4θ – 2sin2θ – 1 = 0
sin2θ = `(-(-2) +- sqrt((-2)^2 - 4 xx 1 xx -1))/(2 xx 1)`
= `(2 +- sqrt(4 + 4))/2`
= `(2 +- sqrt(8))/2`
= `(2 +- 2sqrt(2))/2`
= `1 +- sqrt(2)`
∴ sin2θ = `(1 + sqrt(2))` or `(1 - sqrt(2))`
⇒ – 1 ≤ sin θ ≤ 1
⇒ sin2θ ≤ 1 but sin2θ = `(1 + sqrt(2))` or `(1 - sqrt(2))`
Which is not possible.
APPEARS IN
संबंधित प्रश्न
Find the radian measure corresponding to the following degree measure:
– 47° 30'
Find the radian measure corresponding to the following degree measure:
520°
Find the degree measure corresponding to the following radian measure (Use `pi = 22/7`)
-4
A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm
(Use `pi = 22/7`)
In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.
Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length
10 cm
Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length
21 cm
Find the degree measure corresponding to the following radian measure:
(−3)c
Find the degree measure corresponding to the following radian measure:
11c
Find the degree measure corresponding to the following radian measure:
1c
Find the radian measure corresponding to the following degree measure: 135°
Find the radian measure corresponding to the following degree measure: −300°
Find the radian measure corresponding to the following degree measure: 7° 30'
One angle of a triangle \[\frac{2}{3}\] x grades and another is \[\frac{3}{2}\] x degrees while the third is \[\frac{\pi x}{75}\] radians. Express all the angles in degrees.
Find the magnitude, in radians and degrees, of the interior angle of a regular heptagon.
The angles of a triangle are in A.P. and the number of degrees in the least angle is to the number of degrees in the mean angle as 1 : 120. Find the angles in radians.
The number of sides of two regular polygons are as 5 : 4 and the difference between their angles is 9°. Find the number of sides of the polygons.
A rail road curve is to be laid out on a circle. What radius should be used if the track is to change direction by 25° in a distance of 40 metres?
A wheel makes 360 revolutions per minute. Through how many radians does it turn in 1 second?
If D, G and R denote respectively the number of degrees, grades and radians in an angle, the
The angle between the minute and hour hands of a clock at 8:30 is
At 3:40, the hour and minute hands of a clock are inclined at
If OP makes 4 revolutions in one second, the angular velocity in radians per second is
A circular wire of radius 7 cm is cut and bent again into an arc of a circle of radius 12 cm. The angle subtended by the arc at the centre is
The radius of the circle whose arc of length 15 π cm makes an angle of \[\frac{3\pi}{4}\] radian at the centre is
If θ lies in the second quadrant, then show that `sqrt((1 - sin theta)/(1 + sin theta)) + sqrt((1 + sin theta)/(1 - sin theta))` = −2sec θ
“The inequality `2^sintheta + 2^costheta ≥ 2^(1/sqrt(2))` holds for all real values of θ”
The value of cos1° cos2° cos3° ... cos179° is ______.
Which of the following is correct?
[Hint: 1 radian = `180^circ/pi = 57^circ30^'` approx]
State whether the statement is True or False? Also give justification.
`cos (2pi)/15 cos (4pi)/15 cos (8pi)/15 cos (16pi)/15 = 1/16`
