coolkidcringe
Answered

Welcome to Westonci.ca, where curiosity meets expertise. Ask any question and receive fast, accurate answers from our knowledgeable community. Get detailed answers to your questions from a community of experts dedicated to providing accurate information. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

tan(2 sin^-1 0.4)
Find the Exact value

Sagot :

Answer:

tan(2u)=[4sqrt(21)]/[17]

Step-by-step explanation:

Let u=arcsin(0.4)

tan(2u)=sin(2u)/cos(2u)

tan(2u)=[2sin(u)cos(u)]/[cos^2(u)-sin^2(u)]

If u=arcsin(0.4), then sin(u)=0.4

By the Pythagorean Identity, cos^2(u)+sin^2(u)=1, we have cos^2(u)=1-sin^2(u)=1-(0.4)^2=1-0.16=0.84.

This also implies cos(u)=sqrt(0.84) since cosine is positive.

Plug in values:

tan(2u)=[2(0.4)(sqrt(0.84)]/[0.84-0.16]

tan(2u)=[2(0.4)(sqrt(0.84)]/[0.68]

tan(2u)=[(0.4)(sqrt(0.84)]/[0.34]

tan(2u)=[(40)(sqrt(0.84)]/[34]

tan(2u)=[(20)(sqrt(0.84)]/[17]

Note:

0.84=0.04(21)

So the principal square root of 0.04 is 0.2

Sqrt(0.84)=0.2sqrt(21).

tan(2u)=[(20)(0.2)(sqrt(21)]/[17]

tan(2u)=[(20)(2)sqrt(21)]/[170]

tan(2u)=[(2)(2)sqrt(21)]/[17]

tan(2u)=[4sqrt(21)]/[17]

We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Keep exploring Westonci.ca for more insightful answers to your questions. We're here to help.