Question
Asked Nov 4, 2019
Solve the equation for x if 0 s x < 2. Give your answer in radians using exact values only. (Enter your answers as a comma-separated list.)
2 sin x — 3 cot x — 3 csсх 3D 0
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Solve the equation for x if 0 s x < 2. Give your answer in radians using exact values only. (Enter your answers as a comma-separated list.) 2 sin x — 3 cot x — 3 csсх 3D 0

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check_circleExpert Solution
Step 1

The given trigonometric equation is shown below.

2 sin x 3 cotx-3cscx = 0
Also 0x27
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2 sin x 3 cotx-3cscx = 0 Also 0x27

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Step 2

Write all the trigonometric function in terms of sine and cosine.

2sin x 3 cotx-3cscx =0
1
-3
cos x
2sin x-3
sin x
sin x
3
-= 0
sinx
2sin -3
sin x
Simplifying it
2sin2x3cosx-3 = 0
2(1-cos2x)-3 cosx-3=0
2 2 cos2 x3 cos x - 3 = 0
-2 cos2 x-3 cos x - 1= 0
2 cos2 3 cosx +1= 0
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2sin x 3 cotx-3cscx =0 1 -3 cos x 2sin x-3 sin x sin x 3 -= 0 sinx 2sin -3 sin x Simplifying it 2sin2x3cosx-3 = 0 2(1-cos2x)-3 cosx-3=0 2 2 cos2 x3 cos x - 3 = 0 -2 cos2 x-3 cos x - 1= 0 2 cos2 3 cosx +1= 0

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Step 3

The above equation is quadratic in cos x.

Now solve t...

2 cos2 x3
cos x 1= 0
Take cos x = u
2u3u1 0
-3+ v32 -4-2.1
и
2-2
-3t1
и %3
4
1
u-1
2
1
cos x
2
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2 cos2 x3 cos x 1= 0 Take cos x = u 2u3u1 0 -3+ v32 -4-2.1 и 2-2 -3t1 и %3 4 1 u-1 2 1 cos x 2

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Tagged in

Math

Trigonometry