# Thread: [SOLVED] solve using CAST rule

1. ## [SOLVED] solve using CAST rule

Hi,
I was wondering if you could give me some step-by-step instructions for solving for theta here using the CAST rule:
sin theta = -1/2, and theta degrees is < theta < 360 degrees.
(the < symbol also has a line underneath it, which i think means equal. sorry, couldn't write it like it on the keyboard, lol)
i would appreciate any guides you can think of, thank you!

2. Isn't the "CAST Rule" just an awareness of the sign of the basic trigonometric functions?

Positive Sine: Quadrants I and II
Positive Cosine: Quadrants I and IV
Positive Tangent: Quadrants I and III

From a Reference Angle point of view, |sin(x)| = 1/2 produces x = 30º(Quadrant I), 150º (Quadrant II), 210º (Qudarant III), or 330º (Quadrant IV).

Knowing that, in this case, we have sin(x) = -1/2, discard those in Quadrants I and II, since we know the sine to be positive there. This produces x = 210º or x = 330º.

3. thans tkhunny! How do you know that sin x produced 30 degrees in the 1st quadrant, 150 in the 2nd quadrant, etc.? that's the part i'm not sure about.

4. How do you know that sin x produced 30 degrees in the 1st quadrant, 150 in the 2nd quadrant, etc.?
Do you know how a reference angle works?

5. Originally Posted by TKHunny
Isn't the "CAST Rule" just an awareness of the sign of he basic trigonometric functions?

Positive Sine: Quadrants I and II
Positive Cosine: Quadrants I and IV
Positive Tangent: Quadrants I and III

From a Reference Angle point of view, |sin(x)| = 1/2 produces x = 30º(Quadrant I), 150º (Quadrant II), 210º (Qudarant III), or 330º (Quadrant IV).

Knowing that, in this case, we have sin(x) = -1/2, discard those in Quadrants I and II, since we know the sine to be positive there. This produces x = 210º or x = 330º.
Yeah, I have always said A-S-T-C to myself, but never thought of starting from the 4th quadrant to use the word CAST.

6. Originally Posted by colby2152
Yeah, I have always said A-S-T-C to myself, but never thought of starting from the 4th quadrant to use the word CAST.
I use the acronym "All Suckers Take Calculus".

7. Just think about it this way:

In quadrant 2: $\pi$ - Reference Angle

In quadrant 3: $\pi$ + Reference Angle

In quadrant 4: $2\pi$ - Reference Angle

8. went through the qu. a few times and I got it now
sinx-1 = 30
130 + 30 = 210
360-30=330
thank you tkhunny and topher!!