Using the graph of y=sin x, list all the values on the interval [-15π/4,-7π/4] that satisfy the ordered pair (x,1/√2).

Question

Doing trig need a little help

Answer 1

1st and worst way! Remember that sin(x) gives +0.707 at reference angle pi/4 only while in the first and second quadrants. That would be positive pi/4 and 3pi/4. But here we have negative angles going clockwise. Draw your unit circle and find that -15pi/4 falls in quadrant 1. It is almost -4pi which would be -16pi/4. First solution (x=pi/4) which we can call here -15pi/4. Now swing reverse clockwise into quadrant 2 by removing pi/2 and find X= -13pi/4. Last, swing reverse clockwise all way round back into quadrant 1 and find X= -7pi/4 (which looks like pi/4 - a bit less than -2pi or -8pi/4)

Typed up this looks very, very, very confusing. Draw that picture (unit circle) that is worth one thousand words! :-)

2nd way would be to draw your unit circle - clockwise and mark off every reference angle pi/4 in second and first quadrants.

3rd way simply graph Y= sin(X) with a line Y=0.707 in Desmos and plot your solutions.