Question 38809: Book pg.651
Problem 5)
note: ^-means exponent
5) 2sin^2@-sin@-1=0
So far this is what I have:
2sin^2@-sin@-1=0
(2sin@+1)(sin@-1)=0
sin@=1/2 and sin@=1
sin@of -1/2=210degrees and 330degrees, sin@1=90degrees
Solutions:{90, 210, 330 degrees}
How did sin of 1/2 change to -1/2
and
How did the answers of 210degrees and 330degrees come from sin of -1/2
Is there a way I can achieve these two degrees from a calculator? I'm using a Ti-84 silver.
Thanks for your help.
Answer by longjonsilver(2297)   (Show Source):
You can put this solution on YOUR website! OK:
(2sin@+1)(sin@-1)=0 is fine but sin@=1/2 and sin@=1 has an error.
(2sin@+1)(sin@-1)=0
so (2sin@+1)=0 or (sin@-1)=0
2sin@=-1 or sin@=1
sin@=-1/2 or sin@=1
OK... as for answers: your calculators only store one answer for the question "what is the angle...", so you need to learn how to figure out the others, given the range of the possible values of the angle, which should be quoted in the question. Typically this range is from 0 to 360 degrees.
Look at the Lesson i wrote on this topic. It will help you. Here is that method applied to your question for the range 0 to 360 inclusive: check that this is the range given in your question.
First thing: each of sin, cos and tan will cycle every 360 degrees. Within that cycle, you will expect to find 2 angles (for a straight forward angle) that match the question.
Second thing: Best to work with positives first as your calculator is easier to use that way. So:
1. sin@=-1/2
First what angle is sin@=1/2? Use your calculator. It is @=30.
OK... Which of the 4 quadrants has sin negative? LEARN THIS..look at my Lesson. Answer is "sin is negative in the 3rd and 4th quadrants. So, the equivalent angles there to 30 degrees are:
180+30 --> 210
360-30 --> 330
Put both of these into your calc and press sin and confirm that they do give -1/2.
2. sin@=1
OK... use your calculator again. It gives you 90. This is your 1st quadrant answer. Where is sin also positive? Answer 2nd quadrant. So this angle is:
180-90 --> 90 which is the same answer as given by the calculator. So here there is only one answer.
Complete answers are: 90, 210, 330.
Hope this helps?
jon
|
|
|
