(Solved): Consider the following triangles. (i) Find the exact values of the six trigonometric functions of t ...

Consider the following triangles. (i) Find the exact values of the six trigonometric functions of the angle \( \theta \) for the smaller triangle. Find the exact values of the six trigonometric functions of the angle \( \theta \) for the smaller triangle. \[ \sin (\theta)= \] \[ \cos (\theta)= \] \[ \tan (\theta)= \] \[ \csc (\theta)= \] \[ \sec (\theta)= \] \[ \cot (\theta)= \] Find the exact values of the six.trigonometric functions of the angle of for the larger triangle. \[ \begin{array}{l} \sin (\theta)= \\ \cos (\theta)= \\ \operatorname{tsn}(\theta)= \\ \csc (\theta)= \end{array} \] \[ \begin{array}{l} \sin (\theta)= \\ \cos (\theta)= \\ \tan (\theta)= \\ \csc (\theta)= \\ \sec (\theta)= \end{array} \] Explain why the function values are the same. The triangles are congruent, and the trigonometric function values must be the same. The triangles are similar, and corresponding sides are proportional.