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9 October, 12:42

Find the first four positive values of arccos (0.7). I know how to get the first, but as for the rest, I am lost.

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  1. 9 October, 15:58
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    Now cos⁻¹ (0.7) is about 45.6°, that's on the first quadrant.

    keep in mind that the inverse cosine function has a range of [0, 180°], so any angles it will spit out, will be on either the I quadrant where cosine is positive or the II quadrant, where cosine is negative.

    however, 45.6° has a twin, she's at the IV quadrant, where cosine is also positive, and that'd be 360° - 45.6°, or 314.4°.

    now, those are the first two, but we have been only working on the [0, 360°] range ... but we can simply go around the circle many times over up to 720° or 72000000000° if we so wish, so let's go just one more time around the circle to find the other fellows.

    360° + 45.6° is a full circle and 45.6° more, that will give us the other angle, also in the first quadrant, but after a full cycle, at 405.6°.

    then to find her twin on the IV quadrant, we simply keep on going, and that'd be at 360° + 360° - 45.6°, 674.4°.

    and you can keep on going around the circle, but only four are needed this time only.
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