Trigonometry: How to use the ASTC Rule | The Quadrant | CAST

The ASTC Rule or CAST rule:
1. When the angle lies in the first quadrant, then all trigonometric ratios are positive.
2. When the angle lies in the second quadrant, then sine and cosecant are positive while other trigonometric ratios sin,cosec, tan and cot are negative.
3. When the angle lies in the third quadrant, then tangent and cotangent are positive while other trigonometric ratios sin,cosec, tan and cot are negative.
4. When the angle lies in the fourth quadrant, then cosine and secant are positive while other trigonometric ratios sin,cosec, tan and cot are negative.
The first letter of the first word in this phrase is 'A'. This may be taken to indicate that all trigonometric ratios in the first quadrant are positive.
The first letter of the second word S indicates that sine and its reciprocal are positive in the 2nd quadrant.
The first letter of the third word T indicates that tangent and its reciprocal is positive in the third quadrant.
The first letter of the last word C indicates that cosine and its reciprocal are positive in the fourth quadrant.
The Quadrant can be used in trigonometry to find the values special angles which are greater than 90 degrees.
Trigonometry, is a branch of mathematics,
concerned with specific functions of angles and their application to calculations. There are six functions of an angle commonly used in trigonometry. Their names are sine, cosine, tangent, cotangent, secant, and cosecant.
Trigonometric functions are used in obtaining unknown angles and distances from known or measured angles in geometric figures.
A common use of mnemonics is to remember facts and relationships in trigonometry. For example, the sine, cosine, and tangent ratios in a right triangle can be remembered by representing them and their corresponding sides as strings of letters. For instance, the mnemonic is SOH-CAH-TOA
In this video, we are to discuss the trigonometric ratios.
Trigonometric Ratios are applicable only for a right-angle triangle. A right-angle triangle is a special triangle in which one angle is 90° and the other two are less than 90°.
You can watch more videos on my playlist;
• Trigonometry, Trigonom...
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Great teaching! How about for angles 180/270? Do I just have to remember the values for these angles?

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How do you got the last answers like after the -sin45 and -cos30?

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it is supposed to be 1/ root 2 and 2/ root 3

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I don't understand your question.
-sin45° =1/√2
-cos30° =(√3)/2

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√2/2 = √2/√2.√2 = 1/√2