4th

1. Trigonometric
Ratios of Special
Angles
 Find the trigonometric ratios of special
angles

2. Lets play
TRIG𝜃

3. Ready?

4. 𝜃

5. 𝜃

6. Use a protractor to find
the measures of the
angles of each triangle

7. 1.∠𝐴 =______
2. ∠𝐵 =______
3. ∠𝐶 =______
1. ∠𝐷 =______
2. ∠𝐸 =______
3. ∠𝐹 =______
1. ∠𝐿 =______
2. ∠𝑀 =_____
3. ∠𝑁 =_____

8. The following sides of
special right triangles
are related as follows:

11. 45° – 45° – 90° Triangle Theorem
the legs are congruent
the length of the hypotenuse is
times the length of a leg
hypotenuse = leg

12. 30°– 60° – 90° Triangle Theorem
 the length of the hypotenuse is twice the
length of the shorter leg
 the length of the longer leg is times the
length of the shorter leg
 hypotenuse = 2 shorter leg
 longer leg = shorter leg

13. Example 1
𝑚 = 2 ∙ 8
𝑚 = 8 2

14. Example 2

15. Angles
Ratios 0° 30° 45° 60° 90°
sin𝜽
𝒄𝒐𝒔𝜽
𝒕𝒂𝒏𝜽
𝒄𝒔𝒄𝜽
𝒔𝒆𝒄𝜽
𝒄𝒐𝒕𝜽

16. Angles
Ratios 0° 30° 45° 60° 90°
sin𝜽 𝟎 𝟏
𝟐
𝟏
𝟐
𝟑
𝟐
𝟏
𝒄𝒐𝒔𝜽 𝟏 𝟑
𝟐
𝟏
𝟐
𝟏
𝟐
𝟎
𝒕𝒂𝒏𝜽 𝟎 𝟏
𝟑
𝟏 𝟑 𝒖𝒏𝒅𝒆𝒇𝒊𝒏𝒆
𝒄𝒔𝒄𝜽 𝒖𝒏𝒅𝒆𝒇𝒊𝒏𝒆 𝟐 𝟐 𝟐
𝟑
𝟏
𝒔𝒆𝒄𝜽 𝟏 𝟐
𝟑
𝟐 𝟐 𝒖𝒏𝒅𝒆𝒇𝒊𝒏𝒆
𝒄𝒐𝒕𝜽 𝒖𝒏𝒅𝒆𝒇𝒊𝒏𝒆 𝟑 𝟏 𝟏 𝟎