A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
Solution and Explanation
Number of revolutions made by the wheel in 1 minute = 360
∴ Number of revolutions made by the wheel in 1 second = \(\frac{360}{60} = 6\)
In one complete revolution, the wheel turns an angle of 2π radian.
Hence, in 6 complete revolutions, it will turn an angle of 6 × 2π radian, i.e.,
12 π radian
Thus, in one second, the wheel turns an angle of 12π radian.
Top Questions on Trigonometric Functions
- Evaluate the limit: \[ \lim_{x \to 0} \csc{x} \left( \sqrt{2 \cos^2{x} + 3 \cos{x}} - \sqrt{\cos^2{x} + \sin{x} + 4} \right) \] is equal to:
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- The value of \( \cos \left( \sin^{-1} \left(-\frac{3}{5}\right) + \sin^{-1} \left(\frac{5}{13}\right) + \sin^{-1} \left(-\frac{33}{65}\right) \right) \) is:
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If \( \alpha>\beta>\gamma>0 \), then the expression \[ \cot^{-1} \beta + \left( \frac{1 + \beta^2}{\alpha - \beta} \right) + \cot^{-1} \gamma + \left( \frac{1 + \gamma^2}{\beta - \gamma} \right) + \cot^{-1} \alpha + \left( \frac{1 + \alpha^2}{\gamma - \alpha} \right) \] is equal to:
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- Let \( M \) and \( m \) respectively be the maximum and the minimum values of \[ f(x) = 1 + \sin^2 x \cos^2 x + \frac{4 \sin 4x}{\sin^2 x \cos^2 x} \] for \( x \in \mathbb{R} \). Then \( M^4 - m^4 \) is equal to:
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- If \( \alpha>\beta>\gamma>0 \), then the expression \[ \cot^{-1} \beta + \left( \frac{1 + \beta^2}{\alpha - \beta} \right) + \cot^{-1} \gamma + \left( \frac{1 + \gamma^2}{\beta - \gamma} \right) + \cot^{-1} \alpha + \left( \frac{1 + \alpha^2}{\gamma - \alpha} \right) \] is equal to:
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Questions Asked in CBSE Class XI exam
- Consider the reactions:
- H3PO2(aq) + 4 AgNO3(aq) + 2 H2O(l) \(\rightarrow\) H3PO4(aq) + 4Ag(s) + 4HNO3(aq)
- H3PO2(aq) + 2CuSO4(aq) + 2 H2O(l) \(\rightarrow\) H3PO4(aq) + 2Cu(s) + H2SO4(aq)
- C6H5CHO(l) + 2[Ag (NH3)2]+(aq) + 3OH- (aq) \(\rightarrow\) C6H5COO- (aq) + 2Ag(s) + 4NH3(aq) + 2 H2O(l)
- C6H5CHO(l) + 2Cu2+(aq) + 5OH-(aq) \(\rightarrow\) No change observed.
What inference do you draw about the behaviour of Ag+ and Cu2+ from these reactions?
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- If U = {a, b, c, d, e, f, g, h}, find the complements of the following sets:
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(ii) B = {d, e, f, g}
(iii) C = {a, c, e, g}
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Concepts Used:
Trigonometric Functions
The relationship between the sides and angles of a right-angle triangle is described by trigonometry functions, sometimes known as circular functions. These trigonometric functions derive the relationship between the angles and sides of a triangle. In trigonometry, there are three primary functions of sine (sin), cosine (cos), tangent (tan). The other three main functions can be derived from the primary functions as cotangent (cot), secant (sec), and cosecant (cosec).
Six Basic Trigonometric Functions:
- Sine Function: The ratio between the length of the opposite side of the triangle to the length of the hypotenuse of the triangle.
sin x = a/h
- Cosine Function: The ratio between the length of the adjacent side of the triangle to the length of the hypotenuse of the triangle.
cos x = b/h
- Tangent Function: The ratio between the length of the opposite side of the triangle to the adjacent side length.
tan x = a/b
Tan x can also be represented as sin x/cos x
- Secant Function: The reciprocal of the cosine function.
sec x = 1/cosx = h/b
- Cosecant Function: The reciprocal of the sine function.
cosec x = 1/sinx = h/a
- Cotangent Function: The reciprocal of the tangent function.
cot x = 1/tan x = b/a
Formulas of Trigonometric Functions:
