How do you solve #2cos^2theta-4costheta-5=0# in the interval #0<=x<=2pi#?

Question

How do you solve #2cos^2theta-4costheta-5=0# in the interval #0<=x<=2pi#?

1 Answer

Impact of this question

2455 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-10-03T15:59:51

#theta=150.56# deg

Explanation:

#2cos^2theta-4costheta-5=0#. Note that this equation looks like the quadratic equation #2x^2-4x-5=0#. So we will solve using the quadratic formula #x=(-b+- sqrt((b^2-4ac)))/(2a)#
#a=2,b=-4,c=-5#

#costheta=(4+- sqrt(16-4(2)(-5)))/4#

#costheta=(4+-sqrt56)/4#

#costheta=(4+sqrt56)/4# or #costheta=(4-sqrt56)/4#

#theta=cos^-1((4+sqrt56)/4)# or #theta=cos^-1((4-sqrt56)/4)#
#theta=#undefined or #theta=150.56# deg

Science

Math

Humanities

... and beyond

How do you solve #2cos^2theta-4costheta-5=0# in the interval #0<=x<=2pi#?

1 Answer

Explanation:

Related questions

Impact of this question