Section 4.5

Remember, on each problem, your steps are:
a) Isolate the trig function
b) Determine what the argument of the trig function should be for your trig function to have the stated value.
Sometimes c) Determine what the variable must be to make the argument equal to the value(s) found in (b).

Note: Every one of these problems involves our special angles, so these are all non-calculator problems.

#1. sin(x)-1=0.
Step a) Isolate sin(x). Easy, by adding 1 to both sides of the equation. So we get sin(x)=1.
Step b) The argument is x this time (so there is no Step c), so find what x must be to make sin(x) = 1. If we think about one cycle of the sine wave, the graph only hits a height of 1 one time per cycle. That happens to be at /2 (which is at the top of the unit circle, if you think that way). So one solution is x = /2. However, the sine function is 2-periodic, so we must add multiples of 2 onto our answer to get the rest of the answers. Thus our answer is: x = /2 + 2n.

#3. 2*cos(x)-1=0.
Same steps as Problem 1, but this time we need to know when cos(x)=1/2, which happens 2 times per cycle.

#7. 4*cos2(x)-1=0.
This time you must isolate cos(x), but to do that requires a square root. Remember what you must include when you take a square root in an equation.

#9. sec2(x)-2=0.
Same instructions as on #7.

#11. cos(x)*(2*sin(x)+1) = 0.
Notice that you have two things multiplied together to equal zero, so what must be true about the two things? That will launch you into two smaller problems (like #1 & #3) that you will need to solve.

#17. Factor

#21. Convert either sine or cosine to the other one, then factor.

#27. If you can get sine/cosine, that turns into another trig function.

#31. Solve just like #1 & #3, but this time you will have a Step C at the end.

#33. Factor

#39. Solve the same way you did for #1 & #3, though there is a Step C. But then throw out the answers that are not in the interval [0, 2π).

#43. Convert either tangent or cotangent to the other one.

 



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