peterlusambia14th
Answered

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given that sin(x+4)=cos(3x)find tan(x+40)to 4 s.f.​

Sagot :

MrRoyal

Answer:

[tex]\tan(x + 40) = 1.842[/tex]

Step-by-step explanation:

Given

[tex]\sin(x + 4) = \cos(3x)[/tex]

Required

Find [tex]\tan(x + 40)[/tex]

In trigonometry

If [tex]\sin(A) = \cos(B)[/tex]

Then: [tex]A + B = 90[/tex]

So, we have:

[tex]\sin(x + 4) = \cos(3x)[/tex]

[tex]3x + x + 4 = 90[/tex]

[tex]4x + 4 = 90[/tex]

Collect like terms

[tex]4x =- 4 + 90[/tex]

[tex]4x =86[/tex]

Solve for x

[tex]x = 86/4[/tex]

[tex]x = 21.5[/tex]

So:

[tex]\tan(x + 40) = \tan(21.5+40)[/tex]

[tex]\tan(x + 40) = \tan(61.5)[/tex]

Using a calculator:

[tex]\tan(x + 40) = 1.842[/tex]

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