Trigonometrical Functions

The circular wire of diameter 10cm is cut and placed along the circumference of a circle of diameter 1 metre. The angle subtended by the wire at the centre of the circle is equal to
1. π/4 radian
2. π/3 radian
3. π/5 radian
4. π/10 radian
The value of sin²5+sin²10+sin²15+...+ sin²85+sin²90 is equal to
1. 7
2. 8
3. 9
4. 19/2
Ifcos(θ−α)=a,sin(θ−β)=b,then cos²(α−β)+2absin(α−β) is equal to
1. 4a²b²
2. a²-b²
3. a²+b²
4. -a²b²
If x+1/x=2cosθ, then x³+1/x³=
1. cos3θ
2. 2cos3θ
3. 1/2 cos3θ
4. 1/3 cos3θ
If sinx+cosecx=2, then 4sinAsinBsinC is equal to
1. 2
2. 2ⁿ
3. 2ⁿ⁻¹
4. 2ⁿ⁻²
If tanθ=(sinα−cosα)/(sinα+cosα),then sinα+cosα and sinα−cosα must be equal to
1. √2cosθ,√2sinθ
2. √2cosθ,√2cosθ
3. √2sinθ,√2sinθ
4. √2cosθ,√2cosθ
√3cosec20−sec20=
1. 2
2. 2sin20 / sin40
3. 4
4. 4sin20 / sin40
tanα+2tan2α+4tan4α+8cot8α=
1. tanα
2. tan2α
3. cotα
4. cot2α
sin20°sin40°sin60°sin80°=
1. -3/16
2. 5/16
3. 3/16
4. -5/16
If cos⁶α+sin⁶α+Ksin²2α=1, then K =
1. 4/3
2. 3/4
3. 1/2
4. 2
In a ΔABC,if a=2x,b=2yand ∠C=120, then the area of the triangle is
1. xy
2. xy√3
3. 3xy
4. 2xy
The general solution of sinx−3sin2x+sin3x= cosx−3cos2x+cos3x is
1. nπ+π/8
2. nπ/2 + π/8
3. n/π+π/8
4. nπ
If cosθ+cos7θ+cos3θ+cos5θ=0, then θ`
1. nπ/4
2. nπ/4
3. nπ/8
4. None
If sec4θ−sec2θ=2, then the general value of θ is
1. (2n+1)π/4
2. (2n+1)π/10
3. nπ+π/2 or nπ/5 + π/10
The solution set of (5+4cosθ)(2cosθ+1)=0in the interval [0,2π] is
1. {π/3,2π/3}
2. {π/3,π}
3. {2π/3,4π/3}
4. {2π/3,5π/3}
The number of pairs (x, y) satisfying the equations sinx+siny=sin(x+y) and |x|+|y|=1is
1. 2
2. 4
3. 6
4. ∞
If in a triangle ABC, sinA/4=sinB/5=sinC/6, then the value of cosA+cosB+cosCis equal to
1. 69/48
2. 96/48
3. 48/69
4. None
In ΔABC, a(bcosC−ccosB)=
1. a²−b²
2. b²−c²
3. c²−a²
4. a²+b²+c²
If a, b, care the sides of a triangle ABC, then which of the following inequalities is not true
1. 8abc≤(a+b)(b+c)(c+a)
2. 6abc≤bc(b+c)+ca(c+a)+ab(a+b)
3. abc≤(a+b−c)(b+c−a)(c+a−b)
4. None
If x=sin130cos80,y=sin80cos130,z=1+xy,which one of the following is true
1. x>0,y>0,z>0
2. x>0,y<0,0<z<1
3. x>0,y<0,z>1
4. x<0,y<0,0<z<1
2cos x cos y =
1. cos ( x + y) + cos ( x – y)
2. cos (x + y) – cos (x – y)
3. sin (x + y) + sin (x – y)
4. sin (x + y) – sin (x – y)
2sin x cos y=
1. cos ( x + y) + cos ( x – y)
2. cos (x + y) – cos (x – y)
3. sin (x + y) + sin (x – y)
4. sin (x + y) – sin (x – y)
2 cos x sin y =
1. cos ( x + y) + cos ( x – y)
2. cos (x + y) – cos (x – y)
3. sin (x + y) + sin (x – y)
4. sin (x + y) – sin (x – y)
– 2sin x sin y =
1. cos ( x + y) + cos ( x – y)
2. cos (x + y) – cos (x – y)
3. sin (x + y) + sin (x – y)
4. sin (x + y) – sin (x – y)
Convert 6 radians into degree measure
1. 333° 18′ 11″ approximately
2. 340° 28′ 11″ approximately
3. 343° 38′ 11″ approximately
4. None
Find the radius of the circle in which a central angle of 60° intercepts an
arc of length 37.4 cm
1. 36.7 cm
2. 35.7 cm
3. 36 cm
4. 33 cm
The minute hand of a watch is 1.5 cm long. How far does its tip move in
40 minutes?
1. 6.28 cm.
2. 7.28 cm.
3. 8 cm.
4. None
Find the value of cos (–1710°).
1. 1
2. 2
3. 3
4. 0
Find the value of sin 31π/3 .
1. √3
2. 2/√3
3. √3/2
4. 0
Find the value of sin 15°
1. (√3-1)/(√2)
2. (√3-1)/(2√2)
3. (√3)/(2√2)
4. None

Trigonometrical Functions

Quiz