1+1/sin(alpha) =4 the range is for alpha is from 0 to 360 find alpha???

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1+1/sin(alpha) =4 the range is for alpha is from 0 to 360 find alpha???

I got the first angle as 19.5, however, the marking scheme stated that there is another angle(160.5) can you please explain how they got the second angle

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Answer 1 · 2017-11-17T16:36:13

See below.

Explanation:

We have:

$\frac{sin α + 1}{sin α} = 4$ $(sin alpha + 1)/sinalpha = 4$

$sin α + 1 = 4 sin α$ $sinalpha + 1 = 4sinalpha$

$1 = 3 sin α$ $1 = 3sinalpha$

$sin α = \frac{1}{3}$ $sinalpha = 1/3$

$α = 19.5 and ?$ $alpha = 19.5 and ?$

We know that sine is positive in the first and second quadrants, thus the reference angle for the second value of alpha is going to be $19.5˚$ , or $alpha_2 = 180˚ - 19.5˚ = 160.5˚$ .

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1+1/sin(alpha) =4 the range is for alpha is from 0 to 360 find alpha???

I got the first angle as 19.5, however, the marking scheme stated that there is another angle(160.5) can you please explain how they got the second angle

1 Answer

Explanation:

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