SOLUTION: 1.the equation cos teta -sin teta is equal to? 2. Solve the equation, cos 2 teta - cos teta - 2 = 0, where 0 degree <= teta <= 360 degre

Question 752464: 1.the equation cos teta -sin teta is equal to?
2. Solve the equation, cos 2 teta - cos teta - 2 = 0, where 0 degree <= teta <= 360 degre
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1.the equation cos(theta) -sin(theta) is equal to?
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sqrt(1-sin^2(theta)) - sin(theta)
----
= 1-sin^2(theta) = sin^2(theta)
2sin^2(theta) = 1
sin^2(theta) = 1/2
----
sin(theta) = +-sqrt(2)/2
theta = 45 or 135 or 225 or 315 degrees
==============================================
2. Solve the equation, cos^2(theta)-cos(theta)-2 = 0, where 0 degree <= theta<= 360 degree
---------------------
Factor:
[cos(theta)-2)(cos(theta)+1) = 0
cos(theta) = 2 ; cannot be true as -1<= cos(theta) <=1
cos(theta) = -1
True when theta = 180 degrees
==================================
Since 0<= theta <=160, there are no solutions for your equation.
Cheers,
Stan H.
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