Trigonometry 8 Flashcards
ASCT rule
All sin cos tan rule
ASTC RULE?
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.
Reciprocal of sine
Cosec
Reciprocal of cos
Sec
Reciprocal of tan
Cot
If u take a right angled triangle the sin of one of its acute angles is =
Cos of the other acute angle (complementary)
Relation between sin and cos of two complementary angles
Sin A = Cos(90-A)
Cos A = Sin (90-A)
Relation between tan and cot of two complementary angles
Tan A = cot(90-A)
Cot A = tan(90-A)
Relation between sec and cosec of two complementary angles
Sec A = cosec (90-A)
Cosec A = sec (90-A)
Sin (180 - A) =
Sin A as sin is positive in the second quadrant
Cos ( 180 - A ) =
- cos A
3 systems of measuring angles
Sexagesimal or English system {°}
Centesimal or French system {grades}
Circular system (radians)In sexagesimal system of measuring angles -
A right angle = 90 °
1° = 60 min
1 min = 60 sece
In the French system (centesimal system) one right angle is equal to
100 grades
1 grade = 100 min
1 min = 100 sec
What is a radian
The angle subtended at a circle’s center by an arc of the circle whose length is equal to the radius of the circle.
