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how should i determine the exact measure of all the angles that satisfy the following?

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i need to find (cosθ)$${^2}$$ = 1 in the domain $${-360°≤θ <360°}$$

i know i can use the unit circle and quadrantal angles. however, i'm thrown off by the square because i've never encountered a problem like this before? how should i solve it?

for instance, (cos 180)​$${^2}$$ = -1 isn't possible. however, 180° is a possible answer?

the answers in the textbook are -360°, -180°, 0°, and 180°.

Jan 10, 2019
edited by Guest  Jan 10, 2019

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$$\cos^2(\theta) = 1\\ \text{there are only two values }x \text{ such that }x^2=1\text{, these are}\\ x=1,~x=-1\\ \cos(\theta)=1 \Rightarrow \theta = -360^\circ,~\theta=0^\circ\\ \cos(\theta)=-1 \Rightarrow \theta = -180^\circ,~\theta = 180^\circ$$

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Jan 10, 2019

#1
+5797
+2
$$\cos^2(\theta) = 1\\ \text{there are only two values }x \text{ such that }x^2=1\text{, these are}\\ x=1,~x=-1\\ \cos(\theta)=1 \Rightarrow \theta = -360^\circ,~\theta=0^\circ\\ \cos(\theta)=-1 \Rightarrow \theta = -180^\circ,~\theta = 180^\circ$$
so it's best if i think in terms of $$x$$ when facing a quadratic trig/similar trig equations?