assignment 7.5: solving trigonometric equations\nscore: 90/100 answered 10/12\n× question 6\nscore on last…

assignment 7.5: solving trigonometric equations\nscore: 90/100 answered 10/12\n× question 6\nscore on last try: 0 of 10 pts. see details for more.\nat least one scored part is incorrect. jump to first changable incorrect part.\n> next question get a similar question you can retry this question below\nsolve \\( \\cos ( x ) = 0.84 \\) on \\( 0 \\leq x < 2 \\pi \\).\nthere are two solutions, \\( a \\) and \\( b \\), with \\( a < b \\).\n\\( a = \\)\n\\( b = \\)\ngive your answers accurate to 3 decimal places.\nquestion help: video post to forum

assignment 7.5: solving trigonometric equations\nscore: 90/100 answered 10/12\n× question 6\nscore on last try: 0 of 10 pts. see details for more.\nat least one scored part is incorrect. jump to first changable incorrect part.\n> next question get a similar question you can retry this question below\nsolve \\( \\cos ( x ) = 0.84 \\) on \\( 0 \\leq x < 2 \\pi \\).\nthere are two solutions, \\( a \\) and \\( b \\), with \\( a < b \\).\n\\( a = \\)\n\\( b = \\)\ngive your answers accurate to 3 decimal places.\nquestion help: video post to forum

Answer

Explanation:

Step1: Find the first solution

We know that if (\cos(x)=a), then (x = \cos^{-1}(a)) (principal value). Here (a = 0.84), so (x=\cos^{-1}(0.84)). Using a calculator, (\cos^{-1}(0.84)\approx0.574) (since (0\leq x<2\pi) and (\cos(x)) is positive in the first and fourth quadrants, the first - quadrant solution (A) is (x=\cos^{-1}(0.84))).

Step2: Find the second solution

We use the identity (\cos(x)=\cos(2\pi - x)). The second - quadrant solution (B) is (x = 2\pi-\cos^{-1}(0.84)). Substitute (\cos^{-1}(0.84)\approx0.574) into (2\pi - x). So (2\pi-0.574\approx2\times3.142 - 0.574=6.284 - 0.574 = 5.710).

Answer:

(A = 0.574) (B = 5.710)