Advertisements
Advertisements
Question
If tan θ = `(-4)/3`, then sin θ is ______.
Options
`(-4)/5` but not `4/5`
`(-4)/5` or `4/5`
`4/5` but not `- 4/5`
None of these
Advertisements
Solution
If tan θ = `(-4)/3`, then sin θ is `underline((-4)/5 or 4/5)`.
Explanation:
Since tan θ = `- 4/3` is negative, θ lies either in the second quadrant or in the fourth quadrant.
Thus sin θ = `4/5` if θ lies in the second quadrant or sin θ = `- 4/5`, if θ lies in the fourth quadrant.
APPEARS IN
RELATED QUESTIONS
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)`
`11/16`
Find the degree measures corresponding to the following radian measures (Use `pi = 22/7`)
`(5pi)/3`
Find the degree measure corresponding to the following radian measure (use `pi= 22/7`).
`(7pi)/6`
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
15 cm
Find the degree measure corresponding to the following radian measure:
\[\frac{9\pi}{5}\]
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 radian measure corresponding to the following degree measure:
300°
Find the radian measure corresponding to the following degree measure: 35°
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: 125° 30'
The difference between the two acute angles of a right-angled triangle is \[\frac{2\pi}{5}\] radians. Express the angles in degrees.
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.
Let the angles of the quadrilateral be \[\left( a - 3d \right)^\circ, \left( a - d \right)^\circ, \left( a + d \right)^\circ \text{ and }\left( a + 3d \right)^\circ\]
We know: \[a - 3d + a - d + a + d + a - 2d = 360\]
\[ \Rightarrow 4a = 360\]
\[ \Rightarrow a = 90\]
We have:
Greatest angle = 120°
Now,
\[a + 3d = 120\]
\[ \Rightarrow 90 + 3d = 120\]
\[ \Rightarrow 3d = 30\]
\[ \Rightarrow d = 10\]
Hence,
\[\left( a - 3d \right)^\circ, \left( a - d \right)^\circ, \left( a + d \right)^\circ\text{ and }\left( a + 3d \right)^\circ\] are
Angles of the quadrilateral in radians =
The angles of a triangle are in A.P. such that the greatest is 5 times the least. 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 railway train is travelling on a circular curve of 1500 metres radius at the rate of 66 km/hr. Through what angle has it turned in 10 seconds?
Find the distance from the eye at which a coin of 2 cm diameter should be held so as to conceal the full moon whose angular diameter is 31'.
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
Find the value of `sqrt(3)` cosec 20° – sec 20°
Prove that `(sec8 theta - 1)/(sec4 theta - 1) = (tan8 theta)/(tan2 theta)`
The value of tan1° tan2° tan3° ... tan89° 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.
The equality sinA + sin2A + sin3A = 3 holds for some real value of A.
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`
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.
