Question

Using your calculator and rounding your answer to the nearest hundredth, find the remaining trigonometric ratios of Θ based on the given information

sinΘ= 0.23 and Θ∈QI

Answer 1

`\bf sin(\theta)=\cfrac{opposite}{hypotenuse}\\\\ -----------------------------\\\\ 0.23\implies \cfrac{0.23}{1}\implies sin(\theta)=\cfrac{opposite=0.23}{hypotenuse=1} \\\\ \textit{so we now know, what the hypotenuse and opposite side are}\\ \textit{let us use them, to get the adjacent side}\\ \textit{using the pythagorean theorem} \\\\ c^2=a^2+b^2\implies \pm√(c^2-b^2)=a\qquad \begin{cases} c=hypotenuse\\ b=opposite\\ a=adjacent \end{cases}`

now, notice, the pythagorean theorem, can give you a +/- value from the radical... .but we know, the angle in in the Q1or first quadrant,
on the first quadrant, the sine, cosine and tangent are all positive
so the cosine value from the radical there, will then be positive

once you have all three sides, use them in your trig ratios