**Express each of the following in terms of a reference angle.**29.) a. \(\sin 128^\circ\) b. \(\cos 128^\circ\) c. \(\sin (-37^\circ)\) d. \(\cos 500^\circ\) 30.) a. \(\sin 310^\circ\) b. \(\cos 310^\circ\) c. \(\cos (-53^\circ)\) d. \(\sin 1000^\circ\)

Disclaimer: “Since you have asked multiple question, we will solve the first question for you. If you want any specific question to be solved then please specify the question number or post only that question.” Concept: The reference angle is formed by the terminal side of the provided angle with the x-axis at its smallest feasible angle. The angle is always sharp (except when it is exactly 90 degrees). No matter which way the reference angle falls on the axis, it is always positive.Solution: Part(29a): We have angle θ=128° The reference angle for 90°<θ<180° is 180°-θ=180°-128°=52° Hence sin128°=sin52° Part(29b): We have angle θ=128° The reference angle for 90°<θ<180° is 180°-θ=180°-128°=52° Hence cos128°=cos52° Part(29c): sin(-37°) Since sin(-x)=-sinx Therefore we have angle θ=37° The reference angle for 0°<θ<90° is θ=37° Hence sin(-37)°=-sin37° Part(29d): We have angle θ=500° The reference angle for θ<360° is 180°-(θ-360)°=180°-(500-360)°=180°-140°=40° Hence cos500°=cos40°