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# C2: CAST (Trigonometry)

Maths and statistics discussion, revision, exam and homework help.

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1. Re: C2: CAST (Trigonometry)
(Original post by isp)
I know how to use the cast when certain values are given, although, how would you figure out the second value if the first principle value is inbetween regions?

Eg) sinx = 0

x = 0

What would the second value be as this is inbetween regions?

I was taught to draw out the relevant graph and find the values from there.

So in this case, I would draw the sin graph and then find the values for x, which are 0, 180 and 360 (if the range was 0=<x=<360)
2. Re: C2: CAST (Trigonometry)
Using the CAST Method.

sinx = 0
=> x = 0

Where sin is positive:
1st: x = 0
2nd: x = 180 - 0 = 180

x= 0, 180

It's exactly the same as any other value.
3. Re: C2: CAST (Trigonometry)
(Original post by Astonix)
Using the CAST Method.

sinx = 0
=> x = 0

Where sin is positive:
1st: x = 0
2nd: x = 180 - 0 = 180

x= 0, 180

It's exactly the same as any other value.
What about for tan x = 0

=> x = 0

where tan is positive:
1st: x = 0
2nd: x = 180 + 0 = 180

and for cosx = 0

=> x = 90

where cos is positive:
1st: x = 90
2nd: x = 360 - 90 = 270

Correct?
4. Re: C2: CAST (Trigonometry)
(Original post by isp)
What about for tan x = 0

=> x = 0

where tan is positive:
1st: x = 0
2nd: x = 180 + 0 = 180

and for cosx = 0

=> x = 90

where cos is positive:
1st: x = 90
2nd: x = 360 - 90 = 270

Correct?
Your values of x are correct, but where tan and cos is positive is wrong.

Tan is positive in the 1st, and 3rd quadrant.
Cos is positive in the 1st and 4th quadrant.

4th: Cos (x = 360 - x)
1st: All (x = x)
2nd: Sin (x = 180 - x)
3rd: Tan (x = 180 + x)
5. Re: C2: CAST (Trigonometry)
remember sin(x) is the vertical y axis... cos(x) is the horizontal x axis. The angle is taken anticlockwise from the positive x axis.

sin(x)=0
x=0,

this means when is the y=0, (sinx=0), well y is 0, when x(the angle)=0 or x(the angle) is 180degrees, or x(the angle) is 360 degrees.

this continues..
so generally to find the second value, you can use the trig identity : (FOR SINX = ...)

x(2) = 180degrees or (pi radians) - x(1)
Then add 360 degrees to x1,x2, till you get your solutions in the desired range.

sin(x)=0
x=0

x(1)/first value = 0
second value (x2) = 180 - 0

x(3) = 0 + 360

x(4) = 180+360
=540 degrees

you can then check whether sin(x1,x2,x3,x4...)=0

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Last updated: May 23, 2012
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