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If sin theta equals to cos theta then find theta in such a way that theta should be greater than than 180 but less than 360?
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If sin theta equals to cos theta then find theta in such a way that th...
Explanation:
To find theta in such a way that it is greater than 180 degrees but less than 360 degrees and sin(theta) = cos(theta), we can use the trigonometric identity sin(theta) = cos(90 - theta).
Using the trigonometric identity:
Since sin(theta) = cos(theta), we can write sin(theta) = cos(90 - theta).
Substitute the given condition:
sin(theta) = cos(theta) = cos(90 - theta).
Equating the expressions:
sin(theta) = cos(90 - theta),
sin(theta) = sin(90 - theta).
Find the possible values of theta:
Since sin(theta) = sin(90 - theta), the angles that satisfy this condition are theta = 90 - theta + 360k, where k is an integer.
For theta between 180 and 360 degrees:
If theta is between 180 and 360 degrees, we can set up the equation 90 - theta + 360k = theta, where k = 1.
Solving for theta:
90 - theta + 360 = theta,
450 = 2theta,
theta = 225 degrees.
Therefore, theta = 225 degrees satisfies the condition sin(theta) = cos(theta) and falls between 180 and 360 degrees.
To find theta in such a way that it is greater than 180 degrees but less than 360 degrees and sin(theta) = cos(theta), we can use the trigonometric identity sin(theta) = cos(90 - theta).
Using the trigonometric identity:
Since sin(theta) = cos(theta), we can write sin(theta) = cos(90 - theta).
Substitute the given condition:
sin(theta) = cos(theta) = cos(90 - theta).
Equating the expressions:
sin(theta) = cos(90 - theta),
sin(theta) = sin(90 - theta).
Find the possible values of theta:
Since sin(theta) = sin(90 - theta), the angles that satisfy this condition are theta = 90 - theta + 360k, where k is an integer.
For theta between 180 and 360 degrees:
If theta is between 180 and 360 degrees, we can set up the equation 90 - theta + 360k = theta, where k = 1.
Solving for theta:
90 - theta + 360 = theta,
450 = 2theta,
theta = 225 degrees.
Therefore, theta = 225 degrees satisfies the condition sin(theta) = cos(theta) and falls between 180 and 360 degrees.
Community Answer
If sin theta equals to cos theta then find theta in such a way that th...
225
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