Question

consider a right triangle with acute angle of measure 0 and cos 0 = 4/5 use Pythagorean identity to write an equation that can be used to find Sim 0 is ( + ( 4/5 = 1

Answer 1

`\begin{gathered} a. \\ \cos \theta=(4)/(5) \\ \cos ^2\theta+\text{ }\sin ^2\theta=\text{ 1} \\ \sin ^2\theta=1-\cos ^2\theta \\ \sin ^2\theta=\text{ 1-(}(4)/(5))^2 \\ \\ \sin ^2\theta=\text{ 1-}(16)/(25) \\ \\ \sin ^2\theta=\text{ }(9)/(25) \\ \\ \sin ^{}\theta=\sqrt[]{\text{ }(9)/(25)} \\ \\ \sin ^{}\theta=\text{ }(3)/(5) \\ \\ \text{The }\sin ^{}\theta\text{ is }(3)/(5) \\ \\ b. \\ \text{tan}\theta=\frac{\sin^{}\theta}{\cos\theta} \\ \\ \text{tan}\theta=(3)/(5)\text{ }(\cdot)/(\cdot)(4)/(5)=(3)/(4) \\ \\ \text{tha tan }\theta\text{ is }(3)/(4) \end{gathered}`