1. Right Triangle Trigonometry
4.3

2. A standard right triangle
hypotenuse
Side opposite
of θ θ
Side adjacent to θ

3. Right Triangle Definitions of Trigonometric Functions
Let θ be an acute angle of a right triangle. Then the six trigonometric functions of the angle θ are defined as follows: sin θ = csc θ= cos θ = sec θ = tan θ = cot θ =

4. Example 1: Evaluating Trig. Functions
Use the triangle to find the exact values of the six trigonometric functions of θ. 4 θ 3

5. Example 2: Evaluating Trig Functions of 45°
Find the exact values of sin 45°, cos 45°, and tan 45°.

6. Example 3: Evaluating Trig. Functions of 30° and 60°
Us the 30/60/90 triangle to find the exact values of sin 60°, cos 60°, sin 30°, cos 30°. 2
60° 1

7. Sines, Cosines, and Tangents of Special Angles
sin 30° = sin = cos 30° = cos = tan 30° = tan = sin 60° = sin = cos 60° = cos = tan 60° = tan = sin 45° = sin = cos 45° = cos = tan 45° = tan = 1

8. NOTE:
Sin 30° = ½ = cos 60°. This is true because 30° and 60° are complementary angles. So, cofunctions of complementary angles are equal. sin (90° - θ) = cos θ cos (90° - θ) = sin θ tan (90° - θ) = cot θ cot (90° - θ) = tan θ sec (90° - θ) = csc θ csc (90° - θ) = sec θ

9. Fundamental Trigonometric Identities
Reciprocal Identities Sin θ = csc θ = Cos θ = sec θ = Tan θ = cot θ = Quotient Identities tan θ = cot θ = Pythagorean Identities sin2θ + cos2θ = tan2θ = sec2θ 1 + cot2θ = csc2θ

10. Example 4: Applying Trig. Identities
Let θ be an acute angle such that sin θ = .6. Find the values of A) cos θ and B) tan θ using trigonometric identities.

11. Example 5: Using Trig. Identities
Use trigonometric identities to transform one side of the equation into the other. (Prove the statement is true!)
cos θ∙sec θ = 1
(sec θ + tan θ)(sec θ – tan θ) = 1