Hints for "Written Exercises"

SO I have decided not to put any answers up, but if you CAN ALWAYS check to see if you got the right answers by plugging each side of the equation into your calculator and calculating the intersection points. Make sure you are using the right mode and window.

Here are hints for each problem (13+):
(13) Write sec as 1/cos and move to the other side. Combine the fractions and set numerator equal to zero.

(15) sec=1/cos, csc=1/sin, combine like 13

(17) Square root of both sides, don't forget +/-. Take reciprocal of both sides.

(19) sin2x=2sinxcosx, factor

(21) cos2x=2cos²x−1, move all to the left, factor trinomial

(23) w=2θ

(25) factor

(27) cos2x=1−2sin²x, factor - you may get a "no solution" factor

(29) w substitution, square root

(31) w=3x

(33) w=2θ, then you have sin2w=cosw, use double angle formula sin2x=2sinxcosx, move all to the left, factor. This one's tricky.

(35) sin2x=2sinxcosx, multiply both sides by sinx, push cos to the left and factor

(37) cos2x=1−2sin²x

(39) w=2θ+10, then solve for x after you get w. Not as hard as you think...

(41) same tactic as 39

(43) Use graphing calc for now....might be easiest to use angle sum/difference formulas, which we haven't learned yet....any better ideas post them here

(45) cos2x=1−2sin²x, use quadratic formula (!)


If you need clarification on any of this feel free to comment here and I'll respond as soon as I can. I'll be moonlight bowling tonight though, so you may not hear back until late tonight or tomorrow.