TRIGONOMETRY Flashcards
Sine of some angle theta is equal to the opposite side (Opp) divided by the hypotenuse (Hyp).
SOH
Cosine is equal to the adjacent side (adj) divided by the hypotenuse (Hyp).
CAH
Tangent ratio is equal to the opposite side (Opp) divided by the adjacent side (adj).
TOA
In a typical trig. course, these four are the most common that you’ll see: ( special right triangles)
- 3, 4, 5
- 5, 12, 13
- 8, 15, 12
- 7, 24, 25
If you don’t have a special right triangle, then you have no choice but to use ________________ to find the missing side.
Pythagorean Theorem
Fundamental relation in Euclidean geometry between the three sides of a right triangle.
Pythagorean Theorem
Helps us find the missing side length of a right triangle.
Pythagorean Theorem
Can be expressed as, c²= a² + b²; where ‘c’ is the hypotenuse and ‘a’ and ‘b’ are the two legs of the triangle.
Pythagorean Theorem
Defined as the ratio of the side of the angle opposite the angle divided by the hypotenuse.
SIN (Sine)
The ______ rule is used when we are given either a) two angles and one side, or b) two sides and a non-included angle
SIN (Sine)
_______ of an angle, in a right-triangle, is equal to the ratio of adjacent side of that angle and hypotenuse of the triangle.
COS (Cosine)
The ________ rule is used when we are given either a) three sides or b) two sides and the included angle.
COS (Cosine)
Equal to the length of the adjacent side divided by the length of hypotenuse.
COS (Cosine)
The trigonometric ratio between the adjacent side and the opposite side of a right triangle containing that angle.
TAN (Tangent)
Is the ratio of the opposite side over the adjacent side.
TAN (Tangent)
Is the reciprocal of the sine (1 over sine). If sine is equal to 7/12, then cosecant is going to be 25/7.
CSC (Cosecant)
Is the reciprocal of cosine.
SEC (Secant)
Reciprocal of the tangent ratio.
COT (Cotangent)
Pi is equal to?
180°
Pi over 2 is basically the 180 divided by 2 so that’s _____.
90°
In quadrant ___, cosine is equal to a negative value and sine is positive.
Quadrant 2 (Q2)
The ___ value is positive in quadrant 2. The ___value is negative (it’s in negative axis).
Y value, X value
The smallest possible angle made by the terminal side of the given angle with the x-axis.
Reference Angle
It is always an acute angle (except when it is exactly 90 degrees). Is always positive irrespective of which side of the axis it is falling. Same as the as the angle in quadrant 1 (Q1).
Reference Angle
Same as it’s own angle.
Quadrant 1 (Q1)
How to calculate the Reference Angle in Quadrant 2:
The ______ between 180° and the _____ in Quadrant 2.
Difference, Angle
How to calculate the Reference Angle in Quadrant 3:
________ between the angle in quadrant 3 and ___°
Difference, 180°
How to calculate the Reference Angle in Quadrant 4:
360 minus the angle in ________.
Quadrant 4
Sine, cosine, tangent are all positive.
Quadrant 1 (Q1)
Only sine is the positive. Cosine and tangent are both negative.
Quadrant 2 (Q2)
Only tangent is positive. Sine and cosine are both negative.
Quadrant 3 (Q3)
Cosine is only positive. Sine and tangent are negative.
Quadrant 4 (Q4)
______ is relative to y value. So whenever y is positive, _____ will be positive.
Sine
_______ is associated with the x value. X is
positive on the right side, so in quadrants 1 and 4 ______ is positive.
Cosine
_______ is basically relative to y over x so tangent is always negative when sine and cosine do not have the same value. That is why ______ is positive in Q1 and Q3, because they have the same value.
Tangent
Are angles that share the same terminal side.
Coterminal Angles
