1. Geo/Trig
3/9/18

2. Directions for Today…
Happy Friday everyone!
Hope you enjoyed your two snow days!
You’re quiz will be on Monday next week.
Today you will go through a new lesson on Inverse Trig Ratios.
You will then have time to complete extra practice to review for the quiz.
READ THROUGH THE EXAMPLES AND SLIDES VERY CAREFULLY! I HAVE TYPED WHAT I WOULD BE SAYING TO YOU IN CLASS. SO READING THROUGH THIS INFORMATION IS LIKE LISTENING TO ME IN CLASS!

3. Overview of Today… Agenda: Warm-up Check and correct HW
Inverse trig ratios notes
Extra practice for quiz
Goal: I can solve for a missing angle measure using inverse trig. ratios.
Homework: prepare for 9.4 – 9.5 Quiz on Monday

4. Warm-up: complete on your warm-up sheet. Today’s date is 3/9 1
Warm-up: complete on your warm-up sheet. Today’s date is 3/9 1. ABDE is a square. ∆𝐵𝐶𝐷 is equilateral. Calculate the value of x. 𝐶𝐹 is an altitude.

5. Check HW

6. Check HW

7. Check HW

8. Check HW

9. Check HW

10. Check HW

11. Check HW

12. Check HW

13. 9.6 Notes – copy onto notebook paper
Inverse Functions (operations) UNDO each other.
(Ex. × & ÷, + & −, squaring and )
Every trig ratio has an inverse.
𝒔𝒊 𝒏 −𝟏 = inverse sine
𝒄𝒐 𝒔 −𝟏 = inverse cosine
𝒕𝒂 𝒏 −𝟏 = inverse tangent
Inverse Trig Ratios let us take two known sides of a right triangle and find an unknown angle.

14. 9.6 Notes – copy onto notebook paper
Inverse Trig Ratios in the Calculator
Ex. 1:
𝒔𝒊 𝒏 −𝟏 𝟏 𝟐 = _______ → We are asking the calculator what is the measure of the angle that has a sine ratio of 𝟏 𝟐 ?
To put into calculator:
 1) press 2nd
2) Press the trig ratio you want the inverse of (for Ex. 1 it’s sine)
3) Enter the ratio (for Ex. 1 it’s 𝟏 𝟐 )
4) Close the )
5) Hit enter – for Ex. 1 the calculator should say 30. This means that the angle that has a sine ratio of 𝟏 𝟐 is 𝟑𝟎°.

15. 9.6 Notes – copy onto notebook paper
Trig Ratios in the Calculator
Ex. 2
𝒕𝒂 𝒏 −𝟏 𝟏 = ________ → We are asking the calculator what is the measure of the angle that has a tangent ratio of 1?
Try entering this in the calculator to see what angle you get.

16. 9.6 Notes – copy onto notebook paper
Use Inverse Trig Ratios to Finding Missing Angles:
Label the sides based on the missing angle.
Pick your trig ratio based on the sides you know.
Set up the equation.
Solve using inverse trigonometric ratios (calculator).
Example 3

17. 9.6 Notes – copy onto notebook paper
Example 4
Step 2 – know: opp and adj ⇒ use tan
Step 3 - tan 𝑥 = 8 5
Step 4 – in calc: tan − = 57.99
𝒙=𝟓𝟕.𝟗𝟗°

18. 9.6 Notes – copy onto notebook paper
Example 5
Step 2 – know: opp and adj ⇒ use tan
Step 3 - tan 𝑥 =
Step 4 – in calc: tan-1 (2/5√(3)) = 13.00
𝒙=𝟏𝟑.𝟎𝟎° 𝑥° 2
5 3

19. 9.6 Notes – copy onto notebook paper
Example 6: Calculate the measure of the base angles of isos. ∆ABC.
(Hint: need to draw an altitude from the vertex angle to create a right triangle. 𝐴 3 4 𝐵 𝐶
Step 2 – know: hyp and adj ⇒ use cos
Step 3 - cos 𝐴 = 2 3
Step 4 – in calc: cos-1 (2/3) = 48.19
m∠A=𝟒𝟖.𝟏𝟗°

20. Classwork – complete on notebook paper to turn in
Calculate the missing angle measure. Round to the nearest hundredth.

21. Classwork – complete on notebook paper to turn in
Calculate the missing angle measure. Round to the nearest hundredth.

22. Mixed Trig and Inverse Trig Practice
Determine if you are calculating an angle or a side measure.
Label the triangle with opp, adj, and hyp based on the indicated angle.
Set up a trig equation based on the sides involved in the problem
Solve and round to the nearest tenth.

23. All done? - Complete extra practice problems on website to prepare for quiz