please help ASAP i have a quiz tomorrow and noone to help?

Question

first question: which comes first, sin or cosine when you are talking about a value like, (x,y). would x be sin and y cosine or is it vise versa

second question: today after our teacher annouced that we will be having a quiz, he said that we should memorize identities and values and then he started numbering like 0, 30,45,60,90,180,270 and then he'll be like what's the sin of such and such a number and the answers would be like pie/2 or pie/3. i thought it would be answers like 1/2 or square root of 2/2.

am i making sense. im so lost. is there other values for sin and cosine that have pies in the answer

and could you guess what identities he was talking about coz there seems to be a lot in calculus

thanx for trying but i was trying to say, you know how in precalculus if a teacher asked for cos45 you would say square root of 2/2,
well my teacher had answers that had pie in it and i was wondering how and why and if maybe it was a calculus method

and is anyone 110% certain about the x,y and whether sin or cosine comes first coz i keep getting different answers

Answer 1

I'm sorry you are so lost. Let's try to clear things up
a bit for you.
Question 1: For a point (x,y) on the unit circle
(Circle with radius 1 and center at the origin)
x = cos θ, y = sin θ. What is θ here?
It is the angle that a radius makes with the x-axis.
Let's take a simple example: θ = 30 degrees.
Then x = √3/2, y = 1/2 is a point on the circle x²+y²=1.
Does that help?

Question 2. You are being asked two things here:
1). Converting degrees to radians and vice versa.
Radian measure is just another way of measuring angles
and it will be useful later on for simplifying formulas.
Remember that π radians = 180 degrees.
So, an angle of π/2 would be 90 degrees
and an angle of 30 degrees would be π/6.
On your quiz you might be given an angle in
either measure and asked to find the sin, cos
and tan of that angle.
Can you find the sin, cos and tan of all the angles
in your second question? That's the key to that part.

Finally, identities. There are 3 you should have
at your fingertips.
1). sin² θ + cos² θ = 1.
2). tan θ = sin θ/ cos θ
3). 1 + tan² θ = sec² θ

You will need these identities throughout you
calculus career. Please learn them.
Lots of good luck on your quiz!

Answer 2

In math angle (a) is counted counterclockwise starting from x-axis. In that case if you have a vector of length L then its x coordinate will be Lcos(a) while y coordinate is Lsin(a).

As for 45 degrees angle you've got an answer that this is the same andge as pi/4 radians.

Now, why the cosine of this angle is sqrt(2)/2. Consider right triangle with angle 45. Then second angle is also 45, so this is equilateral triangle and both sides are equal. Let their length is s, then by Pithagorean theorem the hypothenus is h=sqrt(s^2+s^2)=s*sqrt(2) and by definition cos(pi/4) = sin(pi/4) = s/h = 1/sqrt(2) = sqrt(2)/2

Answer 3

The reason you may be seeing pi is because 45 degrees is also pi/4 radians. 360 degrees is 2*pi radians

So, in place of 30, 45, 60, 90 degrees, you can see pi/6, pi/4, pi/3, and pi/2 radians

Going from (x,y) Cartesian coordinates to polar coordinates, you get (r*cos(theta),r*sin(theta)). So, cosine is associated with the x coordinate (abscissa) and sine is associated with the y coordinate (ordinate).

Answer 4

vice versa for your first question. x=cos and y=sin. think of it in the unit circle. cos theta gives you the x-component of the line.

no, you are right. he probably meant that they can be written in the forms of radians. 30 = pi/6 , 45 = pi/4 etc.

you might want to know that cos^2 +sin^2 = 1 and from that, by dividing cos^2 or sin^2 to the equation also gives you two other really helpful identity. also, you might want to remember the sum and difference idendity.

Answer 5

sorry, sin is y and cos x. on the pie part, a circle can be give in 2 ways, either 360 degrees or 2 pi radians. 180 degrees equals pi. 90 degrees equals pi over 2. and so on.