Mary's blog #5 or whatever.

This week we learned about solving for (theta) by using these steps:

1. Pythagorean Identities

2.move everything to sin & cos or tan if possible

3.Algebra to simplify

4. Identities

5. Algebra

Ex.

sec-sinxtanx

there are no identities that apply to this problem so you can move on to step 2

you use the identities to change sec to (1/cosx) and tan to (sinx/cosx)

your new equation is (1/cosx) - sinx(sinx/cosx)

which simplifies to (1/cosx) - (sin^2x/cosx)

which cancels and leaves you with cosx as your answer

8-5

for this section, you follow the same steps but you use inverses

the steps for inverse are

1. divide by a trig function when solving to cancel

2. cancel from the inside of a trig. func.

ex. 2sin^2Θ-1=0

you subtract one on both sides

you get 2sin^2Θ=1

then you divide by to

you get sin^2Θ=1/2

then you square root each side

then you get sin Θ=square root of 1/2

then you take the inverse of 1/2

you get Θ=sin^-1(square of 1/20

and you put that in your calculator and get 45degrees

then you have to move it to each quadrant because when squareroot a number you get a positive and a negative number so you look for the quadrants where sin is positive and negative which means all four quadrants

so your answers are 45, 135, 225, 315

yay!