Right Triangle Trigonometry

Symbols

Theda – Represents the angle measure

Hypotenuse

Opposite Side

Adjacent

Side

Six Trigonometric Ratios

3 Basic Ratios + 3 Reciprocal Ratios What is a reciprocal?

Six Trigonometric Ratios, cont.

Basic Trig. Ratio Sine Cosine Tangent

Reciprocal Trig. Ratio Cosecant Secant Cotangent

It’s a sin to have two c’s.

Three Basic Trig. Ratios

SOH-CAH-TOA

Sine (SOH)

hypotenuse

oppositesin

24 25

7

Cosine (CAH)

hypotenuse

adjacentcos

24 25

7

Tangent (TOA)

adjacent

oppositetan

24 25

7

Cosecant – Reciprocal of Sine

opposite

hypotenusecsc

24 25

7

sin

1csc

(“It’s a sin to have two C’s.”)

Secant – Reciprocal of Cosine

adjacent

hypotenusesec 24 25

7

cos

1sec

Cotangent – Reciprocal of Tangent

opposite

adjacentcot 24 25

7

tan

1cot

Solving for Side Lengths

If given one side and one angle measure, then we can solve for any other side of the triangle.

8

x

65

Solving Right Triangles, cont.

1. Ask yourself what types of sides do you have: opposite, adjacent, and/or hypotenuse?

2. Pick the appropriate trig function to solve for x.

3. Solve for x.

8

x

65

Solving for Side Lengths, cont.

8

x

65

Solving Side Lengths, cont.

7 x

30

Inverse Trigonometric Functions

We can “undo” trig ratios Gives us the angle measurement (theta) Represented by a small –1 in the upper right hand

corner Ex.

2nd button → trig ratio

1sin

Inverse Trigonometric Functions, cont.

60.cos

Inverse Trigonometric Functions, cont.

Experiment: Take the sin–1(0.75) and the csc (0.75). What do you get?

**** sin –1 ≠ csc Ѳ !!!!! ****

Your Turn: Solve for thetaRound to nearest hundredth

50.sin

50.cos 2

3sin

1tan

Solving For Angle Measures

If given two sides of a triangle, then we can solve for any of the angles of the triangle.

54

θ

Solving for Angle Measures, cont.

1. Ask yourself what types of sides do you have: opposite, adjacent, and/or hypotenuse?

2. Pick the appropriate trig function to solve for

3. Solve for using the inverse trigonometric function

54

θ

Solving for Angle Measures, cont.

54

θ

Your Turn:

Complete problems 1 – 6 in the Right Triangle Trigonometry Guided Notes – Part II packet.

Answers

1. 2. 3.

4. 5. 6.