1. Chapter 6: Trigonometry 6.1: Right-Triangle Trigonometry
Essential Question: What are the six trigonometric functions and how are they related?

2. 6.1: Right-Triangle Trigonometry
Angles and Degree Measure
An angle is formed by two rays with a common endpoint
That endpoint is called the vertex
Angles can be labeled by the angle symbol () and the vertex. The angle below may be labeled A
side
vertex
angle A
side

3. 6.1: Right-Triangle Trigonometry
Angles
Measured in degrees
1 degree (°) is 1/360 of a circle
180° is ½ a circle
90° (a right angle) is ¼ a circle
Minutes and seconds
A minute (‘) is 1/60 of a degree
A second (“) is 1/60 of a minute
Hence, 1 second = 1/3600 of a degree
Hint: It may be easier to convert between degree and DMS (Degree – Minute – Second) forms if you think of degrees as hours

4. 6.1: Right-Triangle Trigonometry
Converting between decimal form and DMS form
Write 35° 15’ 27” in decimal form
Divide minutes by 60
Divide seconds by 3600
Add all numbers together

5. 6.1: Right-Triangle Trigonometry
Converting between decimal form and DMS form (part 2)
Write ° in DMS form
The whole number is the degree.
Multiply by 60. The whole number is the minute.
Multiply by 60. The whole number is the second

6. 6.1: Right-Triangle Trigonometry
Similar Triangles and Trigonometric Ratios
Pneumonic Phrase: SOH-CAH-TOA
Learn it, live it, love it
sin (sine) = opposite / hypotenuse
cos (cosine) = adjacent / hypotenuse
tan (tangent) = opposite / adjacent
Reciprocals of trigonometric ratios
csc (cosecant) = 1 / sin = hypotenuse / opposite
sec (secant) = 1 / cos = hypotenuse / adjacent
cot (cotangent) = 1 / tan = adjacent / opposite

7. 6.1: Right-Triangle Trigonometry
Evaluating Trigonometric Ratios
Evaluate the six trigonometric ratios of the angle θ shown below
sin θ = 5 / 13 csc θ = 13 / 5
cos θ = 12 / 13 sec θ = 13 / 12
tan θ = 5 / 12 cot θ = 12 / 5 13 5 θ 12

8. 6.1: Right-Triangle Trigonometry
Evaluating Trigonometric Ratios
Evaluate the six trigonometric ratios of 62° by using the triangle shown below
sin 62° = 3 / 3.4 csc 62° = 3.4 / 3
cos 62° = 1.6 / 3.4 sec 62° = 3.4 / 1.6
tan 62° = 3 / 1.6 cot 62° = 1.6 / 3 3
1.6 θ
62°
3.4

9. 6.1: Right-Triangle Trigonometry
Evaluating Trigonometric Ratios on a calculator
Calculators have buttons to evaluate sin, cos, tan
To get the trigonometric ratio, simply input the angle value into your calculator.
Make sure you are in degree mode
2nd → More → 3rd item down (we’ll be using radians later)
Evaluate the six trigonometric ratios of 20°
sin 20° ≈ csc 20° = 1 / sin 20° ≈
cos 20° ≈ sec 20° = 1 / cos 20° ≈
tan 20° ≈ cot 20° = 1 / tan 20° ≈

10. 6.1: Right-Triangle Trigonometry
Special Angles
For and triangles, we use exact values instead of calculator estimates.
60° 2
45° 1 1
30°
45° 1

11. 6.1: Right-Triangle Trigonometry
Assignment
Page 419
Problems 9 – 31, odd problems
Copy the chart at the top of page 419
Begin to memorize the terms from that chart which are highlighted in blue