Question

Question #0a956

Answer 1

`141.26; 218.74`

Explanation:

cos 2t + 10cos t - 8 = 0
Replace cos 2t by (2cos^2 t - 1):
`2cos^2 t - 1 + 10cost - 8 = 0`
Solve this quadratic equation for cos t:
`2cos^2 t + 10cos t - 9 = 0`.
`D = b^2 - 4ac = 100 + 72 = 172` --> `d = +- 2sqrt43`
There are 2 real roots:
`cos t = -b/(2a) +- d/(2a) = 10/4 +- 2sqrt43)/4`
cos t = 2.5 + 3.28 = 5.78 (Rejected as > 1)# cos t = 2.5 - 3.28 = - 0.78 Calculator and unit circle give: cos t = - 0.78 --> t = +- 141^@26 Co-terminal arc of (-141.26) --> #t = (360) - 141^@26 = 218^@74# Answers for (0, 2pi): #141^@26; 218^@74#