Peterlusambia14thidn
Answered

Find answers to your questions faster and easier with IDNLearn.com. Discover in-depth answers from knowledgeable professionals, providing you with the information you need.

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

Sagot :

MrRoyalidn

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]

We value your participation in this forum. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. Thank you for visiting IDNLearn.com. We’re here to provide accurate and reliable answers, so visit us again soon.