Posted by T.Gracken on October 10, 2002 at 07:46:46:
In Reply to: stinking trig equations posted by karen on October 09, 2002 at 22:34:22:
: I cant solve the following trig equations. I'd appreciate assistance solving any or all of them:
: 1. 2sin(x/2)=1
isolate sin(x/2) to get sin(x/2)=1/2
Now, since sin(T) = 1/2 when T=pi/6 or T=5pi/6 (for 0 < = T < 2pi), then
x/2 = pi/6 + 2pi*n or x/2 = 5pi/6 + 2pi*n for any integer n.
multiply both sides by 2 to get
x=pi/3 + 4pi*n or x=5pi/3 + 4pi*n for any integer n.
NOW! memorize your basic angle values, then either isolate the trig expression or use algebra techniques (such as factoring and the zero product rule). It may also be necessary to rewrite a trig expression using an identity.
But try the rest and show us your work if you want more help.
: 2. secxsinx = 2sinx
: 3. tan^2x=2tanxsinx
: 4. sinx=1+cosx
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