Ask a Question

If 5tanA =4 then find the value of 5sinA+3cosA/sinA-2cosA

0 votes
asked Oct 1, 2013 in Trigonometry by anonymous
   

1 Answer

+6 votes
There is more than one way to solve this. One way is to use trig identities.I will use the following method.

sinA = opposite / hypotenuse

cosA = adjacent / hypotenuse

tanA = opposite / adjacent

If 5tanA = 4 then tanA = 4/5.

This describes a triangle where the opposite is length 4 and the adjacent is length 5.

Let "a" be the opposite, "b" the adjacent and "c" is the hypotenuse.

a = 4

b = 5

From this, derive:

sinA = 4/c

cosA = 5/c

Use these values to rewrite the equation

[5sinA + 3cosA] / [sinA - 2cosA]

[5(4/c) + 3(5/c)] / [(4/c - 2(5/c)]

[20/c + 15/c] / [(4/c - 10/c)]

[35/c] / [-6/c]

Eliminate "c" by multiplying this equation by c/c which is the same as multiplying by 1.

-35/6
answered Oct 2, 2013 by stg1.stewart Inquisitive Expert (21,460 points)
edited Oct 2, 2013 by stg1.stewart

Categories

ExplainPlease on Facebook

75,014 questions

48,874 answers

1,169 comments

84,600 users

CuriousGirl313,480
BobTheAnswerGuy310,070
smartguy111,120
charlie100,740
bbrown97,580
answerwiz94,860
The.Sage93,460
amanda0192,460
kfox83,500
lsmith82,840
...