Given: 0° ? ? < 360°, 2cos²? + 11cos? = -5 If that's puzzling to you, i desire to advise which you utilize a variable to make it much less complicated to ascertain. enable x = cos? 2cos²? + 11cos? = -5 2(cos?)² + 11cos? = -5 2x² + 11x = -5 Now, it basically sounds like a popular polynomial. :) upload 5 to the two factors. 2x² + 11x + 5 = -5 + 5 2x² + 11x + 5 = 0 element. (2x + one million)(x + 5) = 0 undergo in concepts that x = cos?. (2x + one million)(x + 5) = 0 (2cos? + one million)(cos? + 5) = 0 Set each and each element to 0 and resolve. 2cos? + one million = 0 2cos? = -one million 2cos? / 2 = -one million / 2 cos? = -one million / 2 undergo in concepts your unit circle. cos(a hundred and twenty°) = -one million / 2 cos(240°) = -one million / 2 ? = a hundred and twenty° or 240° cos? + 5 = 0 cos? = -5 undergo in concepts your unit circle. cos? can by no skill be decrease than -one million or greater suitable than one million. -one million ? cos? ? one million Throw cos? = -5 out because of the fact that's an invalid answer. answer: ? = {a hundred and twenty°, 240°} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ verify: 2cos²? + 11cos? = -5 while ? = a hundred and twenty° 2(cos²(a hundred and twenty°)) + 11cos(a hundred and twenty°) = -5? 2(-one million / 2)² + 11(-one million / 2) = -5? 2(one million / 4) + 11(-one million / 2) = -5? (one million / 2) + (-11 / 2) = -5? (one million - 11) / 2 = -5? (-10 / 2) = -5? -5 = -5? actual 2cos²? + 11cos? = -5 while ? = 240° 2(cos²(240°)) + 11cos(240°) = -5? 2(-one million / 2)² + 11(-one million / 2) = -5? 2(one million / 4) + 11(-one million / 2) = -5? (one million / 2) + (-11 / 2) = -5? (one million - 11) / 2 = -5? (-10 / 2) = -5? -5 = -5? actual
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Verified answer
tan θ ( tan θ + 1) = tan θ +3
tan^2θ + tan θ = tan θ + 3
tan^2θ = 3
tanθ = +/-sqrt(3)
exact value: Tan 60 = sqrt(3) and tan 120 = - sqrt(3)
θ = 60 or 240 or 120 or 300
tan θ ( tan θ + 1) = tan θ +3.
tan^2 θ = 3
tan θ = + or - 1.732
θ = 60* or 120* or 240* or 300* ans
tan θ ( tan θ + 1) = tan θ +3
tan^2θ + tan θ = tan θ + 3
tan^2θ = 3
tanθ = sqrt(3)
exact value: Tan 60 = sqrt(3)
θ = 60 or 240
hope this helps!
Given: 0° ? ? < 360°, 2cos²? + 11cos? = -5 If that's puzzling to you, i desire to advise which you utilize a variable to make it much less complicated to ascertain. enable x = cos? 2cos²? + 11cos? = -5 2(cos?)² + 11cos? = -5 2x² + 11x = -5 Now, it basically sounds like a popular polynomial. :) upload 5 to the two factors. 2x² + 11x + 5 = -5 + 5 2x² + 11x + 5 = 0 element. (2x + one million)(x + 5) = 0 undergo in concepts that x = cos?. (2x + one million)(x + 5) = 0 (2cos? + one million)(cos? + 5) = 0 Set each and each element to 0 and resolve. 2cos? + one million = 0 2cos? = -one million 2cos? / 2 = -one million / 2 cos? = -one million / 2 undergo in concepts your unit circle. cos(a hundred and twenty°) = -one million / 2 cos(240°) = -one million / 2 ? = a hundred and twenty° or 240° cos? + 5 = 0 cos? = -5 undergo in concepts your unit circle. cos? can by no skill be decrease than -one million or greater suitable than one million. -one million ? cos? ? one million Throw cos? = -5 out because of the fact that's an invalid answer. answer: ? = {a hundred and twenty°, 240°} ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ verify: 2cos²? + 11cos? = -5 while ? = a hundred and twenty° 2(cos²(a hundred and twenty°)) + 11cos(a hundred and twenty°) = -5? 2(-one million / 2)² + 11(-one million / 2) = -5? 2(one million / 4) + 11(-one million / 2) = -5? (one million / 2) + (-11 / 2) = -5? (one million - 11) / 2 = -5? (-10 / 2) = -5? -5 = -5? actual 2cos²? + 11cos? = -5 while ? = 240° 2(cos²(240°)) + 11cos(240°) = -5? 2(-one million / 2)² + 11(-one million / 2) = -5? 2(one million / 4) + 11(-one million / 2) = -5? (one million / 2) + (-11 / 2) = -5? (one million - 11) / 2 = -5? (-10 / 2) = -5? -5 = -5? actual
tan ² Ө = 3
tan Ө = ± √3
Ө = 60 ° , 120 ° , 240° , 300 °