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# The Trigonometric Functions - PowerPoint PPT Presentation

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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## PowerPoint Slideshow about ' The Trigonometric Functions' - cora-moses

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Presentation Transcript

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

sin  = +

cos  = +

tan  = +

csc  = +

sec  = +

cot  = +

sin  = +

cos  = -

tan  = -

csc  = +

sec  = -

cot  = -

sin  = -

cos  = -

tan  = +

csc  = -

sec  = -

cot  = +

y

x

sin  = -

cos  = +

tan  = -

csc  = -

sec  = +

cot  = -

y

x

• 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.

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

• 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)

• Reciprocal Identities

• QuotientIdentities

• Pythagorean Identities

• The fundamental Pythagorean identity:

• Divide the first by sin2x :

• Divide the first by cos2x :