Answer to Question #236953 in Trigonometry for ari

Question

Write the following in terms of cos x only, if the answer needs a ± don't list both functions, just answer the multiple choice portion appropriately

Answer 1

$1. \ sin^2x+cos^2x=1\\ \Rightarrow sin^2x=1-cos^2x\\ \Rightarrow sinx=\pm\sqrt{1-cos^2x}\\ \\ 2. \ tanx=\frac{sinx}{cosx} \\ \Rightarrow tanx=\pm\frac{\sqrt{1-cos^2x}}{cosx}\\ 3. \ secx =\frac{1}{cosx}\\ 4. \ cosecx=\frac{1}{sinx}=\pm\frac{1}{\sqrt{1-cos^2x}}\\ 5.\ cotx=\frac{1}{tanx}=\frac{cosx}{sinx}=\pm\frac{cosx}{\sqrt{1-cos^2x}}$