This document outlines the six trigonometric ratios: sine, cosine, tangent, secant, cosecant, and cotangent, along with their definitions and applications in right triangles. It includes instructions for using scientific calculators to find trigonometric values and convert between decimal degrees and degrees-minutes-seconds (DMS). Additionally, it provides practice exercises and resources for further study.

1. THE SIX
TRIGONOMETRIC RATIOS
Prepared By:
Mr. Leo Mar DG. Escorpion, LPT

2. MELCS Competencies
• M9GEIVa-1: Illustrates the six trigonometric ratios: sine, cosine, tangent,
secant, cosecant, and cotangent.
• I can illustrate the six trigonometric ratios: sine, cosine, tangent, secant,
cosecant, and cotangent.
• I can convert degrees to decimal degrees or DMS and vice versa.
Topic Learning Targets

3. SOH-CAH-TOA &
CHO-SHA-CAO

4. Trigonometry is the branch of mathematics concerned with
specific functions of angles and their application to
calculations.
Soh-Cah-Toa
Sine
sinθ =
opp
hyp
Cosine
cosθ =
adj
hyp
Tangent
tanθ =
opp
adj
Cho-Sha-Cao
Cosecant
cscθ =
hyp
opp
Secant
secθ =
hyp
adj
Cotangent
cotθ =
adj
opp

5. Reciprocal Identities

6. The adjacent and opposite sides of a right triangle are
interchangeable. It depends upon the location of the given
angle (theta).
θ
opp
adj
hyp θ
opp
adj
hyp

7. Determine the six trigonometric ratios of the given figure.
sinθ =
4
5
cosθ =
3
5
tanθ =
4
3
cscθ =
5
4
secθ =
5
3
cotθ =
3
4

8. Determine the six trigonometric ratios of the given figure.
sinA =
7
25
cosA =
24
25
tanA =
7
24
cscA =
25
7
secA =
25
24
cotA =
24
7

9. Determine the six trigonometric ratios of the given figure.
sinB =
24
25
cosB =
7
25
tanB =
24
7
cscB =
25
24
secB =
25
7
cotB =
7
24

10. SCIENTIFIC CALCULATOR

11. Steps to RESET your scientific
calculator.
1. Press – SHIFT
2. Press – MODE CLR
3. Press – 3
4. Press – EQUAL
5. Press – AC or OFF

12. Steps to RESET your scientific
calculator.
1. Press – SHIFT
2. Press – 9
3. Press – 1
4. Press – EQUAL
5. Press – AC or OFF

13. How to use scientific calculator to get
trigonometric values?
1. Find the buttons for SIN, COS, TAN.
2. Press the given trig. function, then type the theta or angle.
3. To make degree symbols, press DMS
4. Press SD to make
Find the value of the following. (4 decimals)
1. sin15° =
2. cos32° =
3. tan78° =
0.2588
0.8480
4.7046

14. There are no buttons for CSC, SEC, COT, but we can use
RECIPROCAL IDENTITIES.
cscθ =
1
sinθ
secθ =
1
cosθ
cotθ =
1
tanθ
Find the value of the following. (4 decimals)
1. csc25° =
2. sec66° =
3. cot14° =
2.3662
2.4586
4.0108

15. DECIMAL DEGREES &
DEGREE-MINUTES-SECONDS

16. Degrees, Minutes, Seconds
° Degree 1° = 60 mins
′ Minute 1′ = 60 seconds
′′ Second 1′′
Make the following as STANDARD FORM.
Minutes and Seconds must be less than 60.
1. 40°74′
93′′
Manual
Computation:
40°74′93′′
33′′ 60′′= 1′
75′
15′
60′= 1°
41° ∴ 40°74′
93′′ = 𝟒𝟏°𝟏𝟓′
𝟑𝟑′′
Scientific
Calculator:
Just type the given,
then Press EQUAL.

17. DMS to Decimal Degrees
65°18′45′′ Manual Computation:
65 + 18 + 45
65 +
18
60
+
45
3,600
65 + 0.3 + 0.0125 = 65.3125°
Scientific Calculator:
• Type the given DMS, Press EQUAL.
• Press SHIFT, then DMS
• For some calculators: After you Press
EQUAL, you can use SD to make it decimal.

18. Decimal Degrees to DMS
65.3125° Manual Computation:
65° + 0.3125(60)
65° + 18.75′
65° + 18′ + 0.75(60)
65° + 18′ + 45′′ = 65°18′45′′
Scientific Calculator:
• Type the given decimal degrees, then Press EQUAL.

19. Practice Exercise
Standard Form
1. 72°101′
103′′
2. 89°82′
94′′
3. 56°77′
158′′
Decimal Degrees – DMS
1. 73.7119°
2. 90.3928°
3. 57.3272°
DMS – Decimal Degrees
1. 73°42′
43′′
2. 90°23′
34′′
3. 57°19′
38′′

20. Resources
• Orlando A. Oronce et. al (2019). E-Math Worktext in
Mathematics 9 pg. 382-427.
• Teacher’s Prepared (other examples)

21. THANK YOU 
Prepared By:
Mr. Leo Mar DG. Escorpion, LPT