Find all solutions of the equation in the

jisu61hbke

jisu61hbke

Answered question

2022-04-05

Find all solutions of the equation in the interval [0,2π) (express your answer in terms of k, where k is any integer).
cos2θ+7cosθ=8

Answer & Explanation

Matronola3zw6

Matronola3zw6

Beginner2022-04-06Added 10 answers

Observe that we
cos2θ+7cosθ=8
2cos2θ1+7cosθ=8
2cos2θ+7cosθ9=0
2cos2θ+9cosθ2cosθ9=0
cosθ(2cosθ+9)(2cosθ+9)=0
(cosθ1)(2cosθ+9)=0
cosθ1=0cosθ=1cos0
Writing the general answer, we obtain
θ=2kπ±0=2kπ
2cosθ+9=0cosθ92
this case does not give any solution.
Therefore, the general solution of given equation: cos2θ+7cosθ=8 is
θ=2kπ
where, k is any integer.

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?