Introduction to Trigonometry Basic Trigonometric Functions

Introduction to Trigonometry Basic Trigonometric Functions

What is Trigonometry? The study of triangles Relationship between sides and angles of a right triangle › What is a right triangle? A triangle with a 90⁰ angle 90

Review Right Triangles a In relation to angle a, the sides of the triangle are: adjacent hy e po te nu s 90 ⁰ opposite hypotenuse - always longest side and side across from right angle (90⁰) adjacent - side closest to angle a opposite - side opposite to angle a

Review Right Triangles opposite Label the sides for angle b: s u hypotenuse ?ten o p adjacent hy e opposite ? 90 b adjacent ?

Trigonometric Functions Ratios of the sides in relation to angle a: a adjacent e hy p ot e nu s 90 opposite sine cosine tangent

Trigonometric Functions: SINE abbreviation: sin opposit e hypotenus 0 sin 1 e 3 .866 Example: sin(60 ) sin(a) a adjacent e hy p ot e › nu s 2 Ratio of opposite side to hypotenuse for 60 angle is to 2 (.866 to 1) 90 opposite

Trigonometric Functions: COSINE a adjacent e hy p ot e abbreviation: cos adjacen cos(a) t hypotenus › 0 cos 1 e nu s 90 opposite Example: cos(60 ) 1 .5 2 Ratio of adjacent side to hypotenuse for 60 angle is 1 to 2 (half)

Trigonometric Functions: TANGENT abbreviation: tan tan(a) a adjacent e hy p ot e › 0 tan nu s 90 opposite opposit a edjacen t Example: tan(60 ) 1.732 Ratio of opposite side to adjacent side for 60 angle is to 1 (1.732 to 1)

Trigonometric Functions: REMEMBER: SOH SOH – CAH –TOA TOA Opposite Sine Hypotenuse hy Adjacent p e Cosine ot Hypotenuse en us Opposite Tangent Adjacent adjacent a 90 opposite

Using Trigonometric Functions: For any right triangle: calculate other sides if one side and angle known calculate angle if two sides known 90

Calculating Sides: One Side and Angle Known What is known? angle (50 ) and adjacent side (2) 50 2 Solving for hypotenuse: hyWhich function uses e po te hypotenuse? nu s adjacent and COSIN E 90 opposite

Calculating Sides: One Side and Angle Known What is known? angle (50 ) and adjacent side (2) 50 2 hySolving for hypotenuse : 2 e po 3. te hypotenuse 0.643 11 ncos(50 ) u 1 s hypotenuse 3.111 90 opposite

Calculating Sides: One Side and Angle Known Now we know: angle (50 ) and hypotenuse (3.111) 50 Solving for opposite: Which function uses 3. 11 and hypotenuse? 1opposite 2 SIN E 90 opposite

Calculating Sides: One Side and Angle Known Now we know: angle (50 ) and hypotenuse (3.111) 50 Solving for opposite : opposite 3. 11 sin(50 ) 1 2 3.111 opposite 2.384 90 2.384 opposite .766

Calculating Angle: Two Sides Known What is known? adjacent (3) and opposite (5) Solving for angle (a): a hy Which function uses p e ot adjacent and opposite? en us 3 TANGEN T 90 5

Calculating Angle: Two Sides Known What is known? adjacent (3) and opposite (5) Solving for angle (a): a 30.964 hyp 3 e ot tan(a) .6 en 5 3 *usneed to use inverse tan tan-1(.6) a 30.964 90 5