5.2Trigonometric Functions:

Unit Circle Approach

The unit circle is a circle whose radius is 1 and whose center is at the origin.

Since r = 1:

becomes

(0, 1)

(-1, 0)

(0, -1)

(1, 0)

y

x

(0, 1)

(-1, 0)

(0, -1)

(1, 0)

θ =ty

x

P = (a, b)

Let t be a real number and let P = (a, b) be the point on the unit circle that corresponds to t.The sine function associates with t the y-coordinate of P and is denoted by

The cosine function associates with t the x-coordinate of P and is denoted by

If the tangent function is defined as

If the secant function is defined as

the tangent function is defined as If

If the cotangent function is defined as

(0, 1)

(-1, 0)

(0, -1)

(1, 0)

θ =t radiansy

x

P = (a, b)

If radians, the six trigonometric functions of the angle are defined as

y

x

r

a

b

Theorem

P=(a,b)

(5, 0)

Find the exact value of the remaining five trigonometric functions, given:

meaning

gives

P= (0,1)

x

y

θ

undefined

undefined

P= (1, 0)

P= (a, b)

x} r=1

undefined

undefined

a =1