The Trigonometric Functions What about angles greater than 90°? 180°? The trigonometric functions are defined in terms of a point on a terminal side r.
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The Trigonometric FunctionsWhat about angles greater than 90°? 180°?The trigonometric functions are defined in terms of a
point on a terminal side r is found by using the Pythagorean Theorem:
22 yxr
The Trigonometric FunctionsThe trigonometric values do not depend
on the selected point – the ratios will be the same:
All Star Trig Class Use the phrase “All Star Trig Class” to
remember the signs of the trig functions in different quadrants:
AllStar
Trig Class
All functions are positive
Sine is positive
Tan is positive Cos is positive
The value of any trig function of an angle is equal to the value of the corresponding trigonometric function of its reference anglereference angle, except possibly for the sign. The sign depends on the quadrant that is in.
So, now we know the signs of the trig functions, but what about their values?...
Reference AnglesThe reference angle, reference angle, α, is the angle between the
terminal side and the nearest x-axis:
All Star Trig Class Use the phrase “All Star Trig Class” to
remember the signs of the trig functions in different quadrants:
AllStar
Trig Class
All functions are positive
Sine is positive
Tan is positive Cos is positive
Trig values of quadrantal angles:
0° 90° 180° 270° 360°
0 1 0 –1 0
1 0 –1 0 1
0 undefined 0 undefined 0undefined 0 undefined 0 undefined
1 undefined –1 undefined 1undefined 1 undefined –1 undefined
sin
tan
cos
cot
sec
csc
Trigonometric Identities
Reciprocal Identities
1sin
csc x
x
1cos
secx
x
1tan
cotx
x
sintan
cos
xx
x
coscot
sin
xx
x
Quotient Identities
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