12-2 Trigonometric Functions of Acute Angles

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 reciprocalfunctions 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 trigonometricidentity. 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.