Respuesta :
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Explanation:
sinθ = 3/4
[tex]\begin{gathered} \sin \theta=\frac{opposite}{hypotenuse}\text{ = }\frac{3}{4} \\ \text{opposite = 3} \\ \text{hypotenuse = 4} \end{gathered}[/tex]cos(θ) = adjacent/hypotenuse
we need to find adjacent using pythagoras' theorem:
Hypotenuse² = opposite² + adjacent²
4² = 3² + adj²
16 - 9 = adj²
7 = adj²
adjacent = √7
[tex]\cos \mleft(\theta\mright)=\text{ }\frac{\sqrt[]{7}}{4}[/tex][tex]\begin{gathered} \text{tan}\mleft(\theta\mright)=\frac{opposite}{adjacent} \\ \tan (\theta)\text{ = }\frac{3}{\sqrt[]{7}} \end{gathered}[/tex][tex]\begin{gathered} \text{cot}(\theta)\text{ = }\frac{1}{\tan (\theta)} \\ \cot (\theta)\text{ = }\frac{1}{\frac{3}{\sqrt[]{7}}}\text{ = 1 }\div\text{ }\frac{3}{\sqrt[]{7}}\text{ = 1}\times\frac{\sqrt[]{7}}{3} \\ \cot (\theta)\text{ = }\frac{\sqrt[]{7}}{3} \end{gathered}[/tex][tex]\begin{gathered} \sec (\theta)=\frac{1}{\cos (\theta)}\text{ } \\ \sec (\theta)=\frac{1}{\frac{\sqrt[]{7}}{4}}\text{ = 1}\times\text{ }\frac{\sqrt[]{7}}{4} \\ \sec (\theta)\text{ = }\frac{4}{\sqrt[]{7}} \end{gathered}[/tex][tex]\begin{gathered} \csc (\theta)=\text{ }\frac{1}{\sin (\theta)} \\ \csc (\theta)=\frac{1}{\frac{3}{4}}\text{ = 1}\times\frac{4}{3} \\ \csc (\theta)=\text{ }\frac{4}{3} \end{gathered}[/tex]