Geo/Trig 3/9/18

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!

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

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.

Check HW

Check HW

Check HW

Check HW

Check HW

Check HW

Check HW

Check HW

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.

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°.  

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.  

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

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 −1 8 5 = 57.99 𝒙=𝟓𝟕.𝟗𝟗°

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

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°

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

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

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.

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