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 Discussion: All Topics Topic: Solving Trig. Equations

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 Subject: reply to trig problem Author: Anthony Date: Nov 15 2003

if you still need help then here it is.

the two functions you have here are inverses. So....

sec = 1/cos
csc = 1/sin

the equation then becomes
2(1/cosX) - 7(1/sinX)=0

for this equation to be true 2(1/cosX) has to equal   7(1/sinX)    just like
2-2=0 same thing.

so then
2(1/cosX)=7(1/sinX)

but then we want to get the functions on the same side.

notice that we have sin and cos  if we have sin over cos then it can simplify to
tan right?  yes...
so we multipy the terms first by 2 and 7 just to make it look better and get

2/cosX  =  7/sinX

then multipy both sides of the equation by sinX
this produces

2sinX/cosX  =  7
this simplifies to     2tanX  =  7

divide by 2 and get     tanX  =  7/2

to get what tanX is use you calculator and use to tan^-1 key      that means
X=(7/2)/tan

so type     (7/2) * tan^-1=  ?

I don't have my calculator here so you'll have to work it out from here.  Good
luck

Anthony