1.3 Trigonometric Functions

Consider angle in standard position.

Point P(x,y) on the terminal side (not the origin (0,0))

A triangle is formed which has legs of lengths x and y and

hypotenuse

The definition of the six basic trigonometric functions is

Example

If the terminal side of angle in standard position passes through the point P(x,y). Find the values of the six trig functions.

1) P = (12,5)

2) P = (8,-6)

Note: Try with a different point on the terminal ray, say (4,-3) and find the six trig functions. The resultant ratios are the same because of the similar triangles.

Finding Trig values if terminal side defined by Equation of a Line

Find the six trig functions of angle if the terminal side is defined by

Note: If the equation of the line is in form, then

Quadrantal Angles

Find all six trig functions if = 180^o

Find sin 0 ^o

Find tan 270 ^o

Find cos 90 ^o