If `theta``` is a standard position angle and cot`theta` =1.85, in which quadrant(s) could `theta` lie? ``

Expert Answers

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You need to evaluate `theta` under the given conditions, hence, you should use the following trigonometric identity, such that:

`1 + cot^2 theta = 1/(sin^2 theta)`

You need to replace `1.85 ` for `cot theta` , such that:

`1 + 1.85^2 = 1/(sin^2 theta) => sin^2 theta = 1/4.4225`

`sin^2 theta = 0.226 => sin theta = +-0.475 => theta ~~28^o`

You need to notice that `cot theta` has the positive value `1.85` only if values of `sin theta` and `cos theta` are either both positive, or both negative, hence, `theta` could lie in the quadrants 1 (sine and cosine are both positive) or 3 (sine and cosine are both negative).

`sin theta = +0.475 => theta ~~ 28^o`  (quadrant 1)

`sin theta =-0.475 => theta ~~ 208^o` (quadrant 3)

Hence, evaluating the possibl quadrants where `theta` may lie yields that `theta` may lie in quadrant 1 or quadrant 3.

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