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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

- 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

- 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

- The reference angle, a, 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

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)

Trig values of quadrantal angles

Trigonometric Identities

- Reciprocal Identities

- Quotient Identities

Trigonometric Identities

- Pythagorean Identities
- The fundamental Pythagorean identity

- Divide the first by sin2x

- Divide the first by cos2x

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