Solving Trigonometic Equations
solve for x :
1)sinx = (4/5)
2) cosx = (-12/13)
I will do the second one.
first of all since the cosine is negative the angle must be in either the second or third quadrants.
To find the "angle in standard position" take arccos(+12/13) to get 22.6º
so x = 180-22.6 = 157.4º
or x = 180 + 22.6 = 202.6º
since the period of cos x is 360º, other answers are obtained by adding integer multiples of 360 to either 157.4 or 202.6.
I had asked you earlier if you knew about the CAST rule, you did not answer.
Mr, what is the CAST rule ?
Mr, what is the CAST rule ?
it helps you to remember in which quadrants a trig ratio is positive.
The letters stand for (C)osine, (A)ll, (S)ine, and (T)an
C goes into fourth, A into first, S into second, and T into the third.
notice you go counterclockwise, knowing that All are positive in the first starts you off
eg. in the third you see T, so the tan is positive, the other two are then negative.
It is a very useful mneumonic.
thanks a lot