In exercises 89-83, use the figure to find a triangle congruent to triangle POM
ID: 3024735 • Letter: I
Question
In exercises 89-83, use the figure to find a triangle congruent to triangle POM that justifies the statements in each exercises. sin(-theta) = -sin theta, cos(-theta), and tan(-theta) = -tan theta sin(180 degree - theta) = sin theta, cos(180 degree - theta) = -cos theta, and tan(180 degree - theta) =- tan theta sin(180 degree + theta) = - sin theta, cos(180 degree + theta) = -cos theta, and tan(180 degree + theta) = tan theta sin(360 degree - theta) = -sin theta, cos(360 degree 0 theta) = cos theta, and tan(360 degree - theta) = -tan theta In Exercise 84-87, use the results of Exercises 80-83. Find sin(-45 degree) and tan(-60 degree). Find sin 135 degree, cos 135 degree, and tan 120 degree. Find sin 225 degree, cos 240 degree, and tan 210 degree. Find sin 315 degree, cos 300 degree, and tan 330 degree. Show that for any angle theta, -1 lessthanorequalto sin theta lessthanorequalto 1 and -1 lessthanorequalto cos theta lessthanorequalto 1. In the figure, show that the triangles POM and QON and congruent. Find coordinates of the point Q. Show that sin(theta + 90 degree) = cos theta. cos(theta + 90 degree) = -sin theta, and tan(theta + 90 degree) = -cot theta. Suppose tan theta - cot theta. Find theta assuming 0 degreeExplanation / Answer
Solution: (85)
sin 135° = sin (180° - 45°) = sin(45°) = sqrt(2) / 2 = 1/sqrt(2)
cos135° = cos(180° - 45°) = - cos(45°) = -1/sqrt(2)
tan120° = tan (180° - 60°) = - tan(60°) = -sqrt(3)
Solution: (87)
sin 315° = sin (360° - 45°) = - sin(45°) = -sqrt(2) / 2 = -1/sqrt(2)
cos300° = cos(360° - 60°) = cos(60°) = -1/2
tan330° = tan (360° - 30°) = - tan(30°) = -1/sqrt(3)