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Trigonometric Functions

Short Answer Type

581.

Find the general expression for all angles whose sine is zero.

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582. Find the general expression for all angles whose tangent is zero.

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583.

Find the general solution or the general expression for all angles, whose cosine is zero.

110 Views

584.

Find the general expression for all the angles whose cotangent is zero.

102 Views

585. Find a general expression for all angles having the same sine, i.e. when sin x = sin y, find the general value of x

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586.

Find general value of x, when cos x = cos y

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587.
To find general value of x when tanx = tany

We have tanx = tany $rightwards double arrow$ $sinx over cosx equals siny over cosy$

$rightwards double arrow$ sinx cosy - cosx siny = 0 $rightwards double arrow$ sin (x - y) = 0

$rightwards double arrow$ $straight x minus straight y space equals space nπ comma$ where $straight n space element of space straight Z$

$rightwards double arrow$ $straight x equals nπ plus straight y comma$ where $straight n space element of space straight Z$

Hence, when tanx = tany,

then general value of x is given by

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COROLLARY: If cotx = coty $rightwards double arrow$ tanx = tany

So, when cotx = coty, then x = $space nπ plus straight y comma$ where $straight n element of space straight Z$