Find other five trig ratios when given tangent (tan) by using right triangle

In this example problem, we are given that our angle theta is an acute angle and a trigonometric trig ratio tangent tan. We use that to set up a right 90 degree triangle, label the sides as opposite opp, adjacent adj, and hypotenuse hyp. The pythagorean theorem is used to find the additional side length. Then we use SOHCAHTOA to find sine sin and cosine cos. After we have sine sin, cosine cos, and tangent tan, we use our reciprocal identities to find cosecant cos, secant sec, and cotangent cot. We rationalize the denominators as well. Each part of this process is explained and written out step-by-step.