Hi Mikethm
Taken from bonkysleuth's
answer
sin (x + 63.434) = 0.632456 (from
sin (x + 63.434) = sqrt 2 / sqrt 5)
Basic angle (or Reference angle), theta
= sin-1 (0.632456)
= 39.232 degrees
Since sin +, so it lies in the 1st and 2nd quadrant,
x + 63.434 = 39.232, 180 - 39.232
x + 63.434 = 39.232, 140.768
x
= 39.232 - 63.434, 140.768 - 63.434
x =
- 24.2 , 77.33
Since x = - 24.2 degrees, it is a negative angle, we will
need to convert it into a
positive angle 360 - 24.2 = 335.8 degrees.
Since x = 77.33 degrees and x = 335.8 degrees are
between 0 degree and 360,
degrees. So, the answers are x = 77.33 degrees and x
= 335.8 degrees
Check Answer :
(a) Substitute x = 77.33
degrees into
sin (x + 63.434) = sin (77.33 + 63.434) = 0.632456
(Correct)
(b) Substitute x = 335.8
degrees into
sin (x + 63.434) = sin (335.8 + 63.434) = 0.632456
(Correct)
(c) Using Mikethm's answer,
substitute x = 423.434 into
sin (x + 63.434) = sin (423.434 +
63.434) = 0.8 (Incorrect)
(Hi Mikethm, you probably have
made a mistake in your answer.)
Thank you for your kind
attention.
Regards,
ahm97sic
No I am not wrong.
sin x + 2 cos x = sq.rt 2
sin x + 2 cos x = sqrt. 5 sin(x +63.434)
sqrt. 5 sin(x +63.434) = sq.rt 2
sin(x +63.434) = sq.rt (2/5)
Basic angle = sin-1 [sq.rt (2/5)]
= 39.232
Solution is in 1st or 2nd quadrant since sin is +ve
Since 63.434 < x + 63.434 <423.4
We will reject the 1st solution of 39.232 (not in range),
accept 140.768 and the 3rd solution of (360+39.232 aka 399.232)
Thus (x+63.434) = 140.768 or 399.232
x = 77. 334 or 335.798
x= 77.3 or 335.8
In addition, we do NOT ever check solutions by using equations
we form (mistakes might already have been made along the way).
Always use the original equation which is sin x + 2 cos x =
sq.rt 2.
I have a >90% distinction rate with students who have been
tutored by me for more than a year before their O levels. A 100% B3
or better for those tutored for >0.5 years. This is based on a
brain dead list of standard approaches for 30 questions which will
definitely cover 80% of the allocated marks... and the R formula is
one of them (prior to 2002 and happily again from this year on).
Those longer than a year manage distinctions because if we have
time, then I encourage them to think why why why which better their
chance of answering the thinking questions (20%)...
By the way, practically all my students failed their A Maths
before I tutor them. I like to tutor students who failed because it
is fun and challenging.
Oh did I mention no one ever failed on me in more than a decade
of tutoring despite me being stubborn and not ever giving up on any
student at all (except those who want to turn up less than once a
week).
