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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 is found by using the Pythagorean Theorem:. The 6 Trigonometric Functions of angle  are:. The Trigonometric Functions.

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The trigonometric functions
The Trigonometric Functions

  • What about angles greater than 90°? 180°?

  • The trigonometric functions are defined in terms of a point on a terminal side

  • ris found by using the Pythagorean Theorem:



The trigonometric functions1
The Trigonometric Functions

  • The trigonometric values do not depend on the selected point – the ratios will be the same:


First Quadrant:

sin  = +

cos  = +

tan  = +

csc  = +

sec  = +

cot  = +


Second Quadrant:

sin  = +

cos  = -

tan  = -

csc  = +

sec  = -

cot  = -


Third Quadrant:

sin  = -

cos  = -

tan  = +

csc  = -

sec  = -

cot  = +

y

x


Fourth Quadrant:

sin  = -

cos  = +

tan  = -

csc  = -

sec  = +

cot  = -

y

x


All star trig class
All Star Trig Class

  • Use the phrase “All Star Trig Class” to remember the signs of the trig functions in different quadrants:

All

Star

All functions are positive

Sine is positive

Trig

Class

Tan is positive

Cos is positive


So, now we know the signs of the trig functions, but what about their values?...

The value of any trig function of an angle  is equal to the value of the corresponding trigonometric function of its reference angle, except possibly for the sign. The sign depends on the quadrant that  is in.


Reference angles
Reference Angles

  • The reference angle, α, is the angle between the terminal side and the nearest x-axis:


All star trig class1
All Star Trig Class

  • Use the phrase “All Star Trig Class” to remember the signs of the trig functions in different quadrants:

All

Star

All functions are positive

Sine is positive

Trig

Class

Tan is positive

Cos is positive


Quadrantal angles terminal side lies along an axis
Quadrantal Angles(terminal side lies along an axis)



Trigonometric identities
Trigonometric Identities

  • Reciprocal Identities

  • QuotientIdentities


Trigonometric identities1
Trigonometric Identities

  • Pythagorean Identities

    • The fundamental Pythagorean identity:

  • Divide the first by sin2x :

  • Divide the first by cos2x :


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