This week we learned how to simplify and prove trig equations by using a mixture of both identities and algebra. Here are some of the relationships you need to look for in order to solve the equations.
Reciprocal Relationships:
cscΘ=1/sinΘ
secΘ=1/cosΘ
cotΘ=1/tanΘ
Relationships with Negatives:
sin -Θ= -sinΘ and cos -Θ= -cosΘ
csc -Θ= -cscΘ and sec -Θ= -secΘ
tan -Θ= -tanΘ and cot -Θ= -cotΘ
Pythagorean Relationships:
sin²Θ+cos²Θ=1
1+tan²Θ=sec²Θ
1+cot²Θ=csc²Θ
Cofunction Relationships:
sinΘ=cos(90°-Θ) and cosΘ=sin(90°-Θ)
tanΘ=cot(90°-Θ) and cotΘ=tan(90°-Θ)
secΘ=csc(90°-Θ) and cscΘ=sec(90°-Θ)
When you get an equation you have to first check to see if there are any identities you can use, if not you go to algebra, after that you go back to your identities and finish the problem. This is really easy you just need to memorize the relationships.
One thing I had trouble with this week and could use some help on however was writing the equation for shifts.
i guess the main thing i can tell you is just follow your steps, but do the opposite.
ReplyDeleteinstead of adding, subtract to find your amplitude (or just divide by 2)
when you look at the graph, for the y-axis, you do the opposite, so if it moves to the right, its negative, left is positive.
the x-axis is regular, move up its positive, down negative.
to find "b", for sin, it is your second point on the graph.
for cos, subtract 1 from the second point on the graph.