# Solve the trigonometric equation in the interval [0, 27t). Give the exact value, if possible; otherwise, round your answer to two decimal places. (Enter your answers as a comma-separated list.)2 cos2(e)19 cos(e) 9 = 0

Question
10 views help_outlineImage TranscriptioncloseSolve the trigonometric equation in the interval [0, 27t). Give the exact value, if possible; otherwise, round your answer to two decimal places. (Enter your answers as a comma-separated list.) 2 cos2(e)19 cos(e) 9 = 0 fullscreen
check_circle

Step 1

The given trigonometric equation is shown below.

Step 2

The above equation is quadratic in cos x.

Now substitute cos θ = u and solve the quadratic equation using quadratic formula. help_outlineImage Transcriptionclose2u19u9=0 Quadratic formula: The solution of a quadratic equation ax bx +x 0 is: -btb-4ac 2a Therefore -19t v19-4.2.9 2.2 -19+289 4 -19 17 = 4 1 -9 1 -9 2 cose But cose can never be less than - 1, thus ignoring - 9 1 .coSe 2 fullscreen
Step 3

Now solving... help_outlineImage Transcriptionclose1 cos x 2 1 cos.x cos cos 3 3 2 27T cos x cos- 3 cos (-x)cos.x If cos x cos y 27T then x 2n7t y 3 2T 4T 107T It gives, x 3 3 3 fullscreen

### Want to see the full answer?

See Solution

#### Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

### Other 