JAMB - Mathematics (1993 - No. 30)
If sin \(\theta\) = cos \(\theta\), find \(\theta\) between 0o and 360o
45o, 225o
135o, 315o
45o, 315o
135o, 225o
Explanation
sin \(\theta\) = cos \(\theta\) 0 \(\leq\) \(\theta\) \(\leq\) 360o
The acute angle where sin \(\theta\) = cos \(\theta\) = 45o
But at the third Quadrant Cos \(\theta\) = -ve; sin \(\theta\) = -ve.
at the 3rd quadrant, value with respect to Q is
(180 + Q) where Q = acute angle
(180 + 45) = 225°
The two solution are 45°, 225°
The acute angle where sin \(\theta\) = cos \(\theta\) = 45o
But at the third Quadrant Cos \(\theta\) = -ve; sin \(\theta\) = -ve.
at the 3rd quadrant, value with respect to Q is
(180 + Q) where Q = acute angle
(180 + 45) = 225°
The two solution are 45°, 225°
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