1. 12-2 Trigonometric Functions of Acute Angles

2. Trigonometric Functions
There are six trigonometric functions for any acute angle θ.
We have already discussed three: y
hypotenuse r
side opposite y θ
side adjacent x x

3. Reciprocal Functions
The three remaining trigonometric functions are reciprocal functions of those previously defined.
The cotangent of θ, written cot θ, equals
The secant of θ, written sec θ, equals
The cosecant of θ, written csc θ, equals

4. Finding Trigonometric Functions
Give the values of the six trigonometric functions of θ. y 7 θ 3 x

5. Find the values of the six trigonometric functions of angle θ.y 15 θ x 9

6. Trigonometric Functions Using a Point
Find the values of the six trigonometric functions of an angle θ in standard position whose terminal side passes through (5, 12).

7. Trig Identities
An equation involving trig function of an angle θ that is true for all values of θ is a trigonometric identity.
For example:
Pythagorean identity r y θ x

8. Using Trig Identities
Find cos θ and tan θ if θ is an acute angle and

9. Find cos Φ if sin Φ =

10. Cofunctions
The sine and cosine are called cofunctions because sin A = cos B and sin B = cos A.
Similarly, sin A = cos (90 - A).
Other pairs of cofunctions: tangent and cotangent, secant and cosecant
sin θ = cos (90 - θ) cos θ = sin (90 - θ)
tan θ = cot (90 - θ) cot θ = tan (90 - θ)
sec θ = csc (90 - θ) csc θ = sec (90 - θ)

11. Using Cofunction Identities
Use the cofunction identities to find the measure of the acute angle θ.
sin θ = cos 25
cot θ = tan 20.