Specialist2024 Exam 2 Section A · Q4CAS active1 mark

Half-angle cosine from a sine value

Given that $\sin(x) = a$ , where $x \in \left(\frac{3\pi}{2}, 2\pi\right)$ , then $\cos\left(\frac{x}{2}\right)$ is equal to

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-\frac{\sqrt{1+\sqrt{1-a^2}}}{\sqrt{2}}

\frac{\sqrt{1-\sqrt{a^2-1}}}{\sqrt{2}}

\frac{\sqrt{1+\sqrt{1-a^2}}}{\sqrt{2}}

-\frac{\sqrt{\sqrt{1-a^2}-1}}{\sqrt{2}}

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