Just need some help or pointers to solve these equations
Solve for 0 ≥ b ≥ 180
a) 3tanb - 5secb = 4
b) 2sinb - cosb = 2
i used auxillary angles for this question but i didnt get the right answer which was 90 and 143 degrees 8 minutes
Thankyou for any help =D
2sinb - cos b = R sin ( b+a)
= R (sin b cos a + sin a cos b)
2 = R cos a
-1 = R sin a
R = root 5
cos a = 2/root5
sin a = (-1)/root 5
therefore a = 333 degrees 26 minutes
root5 sin ( b + 333 degrees 36 minutes) = 2
b + 333degrees 26 minutes = 63 degreees 26 minutes or 116 degrees 34 minutes
yeaa thats my working out, and that DEF. doesnt equal the answer given.
><"" T.T !!!
The problem with the solutions offered so far is that squaring both sides of an equation nearly always runs the risk of introducing unwanted answers, which then need to be eliminated.
For example, Craig's equation
can be factorised to give
(among other possible answers), which just doesn't satisfy the original equation.
great_math's answer of suffers from the same problem: , not .
THSKluv's original approach is the right one to pursue, but it's easier if you use , not :
The other equation can be solved in the same way. Using great_math's original approach, you get:
Now continue, by writing
Can you complete it now?