Question

solve on the interval 0 2pi) 2secx+5=1

Answer 1

Hello

Answer 2

You start by isolating x, as you would in algebra

Answer 3

\[2\sec x + 5 = 1\]
\[2 \sec x = -4\]
\[\sec x = -2\]
Since:
\[\sec = \frac{ 1 }{ \cos }\]
We get:
\[\frac{ 1 }{ \cos x} = -2\]

Answer 4

Do you know what to do from there?

Answer 5

\[1 = -2 \cos x\]
\[\cos x = -\frac{ 1 }{ 2 }\]

Answer 6

@carson035

Answer 7

Do you know what you would do from here?

Answer 8

Cos of what angle = -1/2

Cosine refers to the x coordinate of an angle, and since this is negative, you want to look to the left side of the unit circle (quadrants 2 and 3)

Answer 9

Once you do that, the answer is pretty simple to find

Answer 10

\[x = \frac{ 2 \pi }{ 3 }, \frac{ 4 \pi }{ 3 }\]

Answer 11

These guys

Answer 12

@carson035