Find the value of theta between 0 circ and 360 ... - SS3 Mathematics Trigonometric Identities and Equations Question
Find the value of \(\theta\) between \(0{^\circ}\) and \(360{^\circ}\) satisfying the equation \(\cos^{2}\theta + 2\cos\theta + 1 = 0\)
A
\(0{^\circ}\)
B
\(180{^\circ}\)
C
\(360{^\circ}\)
D
\(0{^\circ}\) and \(360{^\circ}\)
correct option: d
\[\cos^{2}\theta + 2\cos\theta + 1 = 0\]
Let \(P = \cos\theta\)
\[P^{2} + 2P + 1 = 0\]
\[(P - 1)(P - 1) = 0\]
\[P - 1 = 0\]
\[P = 1\]
\[\cos\theta = 1\]
\[\theta = \cos^{- 1}1 = 0{^\circ}or\ 360{^\circ}\]
Thus, \(\theta = 0{^\circ}\ or\ 360{^\circ}\)
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