1. Got ID? to
T2.1a To define and apply the Six Trigonometric Functions to Standard Angles

2. Active Learning Assignment Questions?
OPENER: Solve the following equations.
2x +3 = x = 17
x = x x – 85 = 13x + 58

3. The Legend of SOH CAH TOA
Trigon on my tree.
Trigonometry
Sine language
Hypoten News
Hypotenuse

4. The Six-Trigonometric Functions (Ratios):y
Opposite
Hypotenuse
Adjacent
From geometry, we know similar triangles have the same ratios of sides. What is this length? 1
0.4 3
This is what the 6 trig ratios are based on: combinations of opposite, adjacent, and hypotenuse!
1.2

5. The Six-Trigonometric Functions (Ratios):y
Opposite
Hypotenuse
Adjacent r y x y y r r
Watch carefully! No matter which quadrant the reference angle is in, the x value remain adjacent and the y value remains opposite!

6. * The Six-Trigonometric Functions (Ratios): Hypotenuse Opposite
Adjacent *
Reciprocal Functions: Definitions are reciprocated

7. * The Six-Trigonometric Functions (Ratios):
You will have a definitions quiz on these. This is what you will write on your quiz. (In this exact order.) *
Reciprocal Functions: Definitions are reciprocated

8. Write functions in a “U”!
QUIZ: ON THE SIX TRIG DEFINITIONS (FUNCTIONS, RATIOS, IDENTITIES, ETC.)
Ex: If given 1. _______ = _____ = __
You will write:
Write functions in a “U”!

9. Quadrangle Angles
x y I IV
III II
x y
x y
(0, 0)
90°
x y

10. Find all the EXACT values for the 6 trig functions for 0°
(1, 0)
x, y

11. An easier set of ratios to remember!
30° Reference Angles:
Can we multiply or scale up each side by 2 and still have a similar triangle? II I
An easier set of ratios to remember! 1
30°
III IV

12. Find all the EXACT values of the 6 trig functions for 30°:*
Hyp 2 1
Opp
Adj

13. Let’s look at 150º Find the EXACT values for:IV
III II
Why is the sin 150 ° positive and the others are negative?
Could you do the rest of them?

14. An easier set of ratios to remember!
60° Reference Angles:
Will it have the same ratios as a 30° reference angle? I IV
III II
An easier set of ratios to remember!
30°
60°

15. Find all the EXACT values for the 6 trig functions:
Let’s try 120º (Can we write rules?) *
Find all the EXACT values for the 6 trig functions: ü ü ü

16. An easier set of ratios to remember!
45° Reference Angles:
Can we “scale up” on a 45° reference angle and still have a similar triangle? I IV
III II
An easier set of ratios to remember! 1
45°

17. Find all the EXACT values of the 6 trig functions for 45°:* 1 1 ü ü ü

18. Why is the hypotenuse always positive? Could you do the rest of them?
Let’s look at 225º
Why is the hypotenuse always positive?
Could you do the rest of them?

19. * Which quadrant? Reference angle? Draw a triangle. Ratios?
Let’s write some rules for finding the exact values of trigonometric functions for standard angles. *
Which quadrant?
Reference angle?
Draw a triangle.
Ratios?
Positive or negative?
Trig functions?
Sin Ө

20. Spend less time worrying who’s right and more time on what’s right.
Active Learning Assignment:
Find all 6 trig functions for:
135°, 180°, 240°, AND 330°.
WOW:
Spend less time worrying who’s right and more time on what’s right.