Question

Use the quadratic formula to find all degree solutions and θ if

0° ≤ θ < 360°.

Use a calculator to approximate all answers to the nearest tenth of a degree. (Enter your answers as a comma-separated list. If there is no solution, enter NO SOLUTION.)

2 sin² θ − 2 sin θ − 1 = 0

Answer 1

Given zsinho - 2 sin 0-1 =0 , 0ʻ<0. < 360° substitute u for sino 24-24-ico -biſ 6²-yac O za -(-2) + VE2)*–462)(-1) 2 (12) u= 2 Į v 1 uz 1 V3 u5 ltva, lava sino = 1+ , sino: 14 The range of sine is aleysi, since +63 does not fall in this range, there is no solution.

sino = I-B O= sin-(1-P) O- -21.5 The sine function is positive in second quadrants. To find the solution, subtrat the reference 180° to find the solution in the quadrant . 0 = 180-(-21.5) To= 201.5) the first and second angle from second The period of sino function is 360° so values will repeat every 360 degrees in both directions 0 - 360 + (-21.5) To= 38.5 n 0 - 201.5+ 360n, 338.5+360n, for any integer For given interval os o <360° so = 20115, 338.5