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I need help with Trigonometry problems

Overview of the Unit:

This Trigonometric Unit covers the basics for the functions Sine, Cosine and Tangent along with using the Pythagorean Theorem and 2 types of special right triangles, 30-60-90 and 45-45-90. These types of problems recur constantly on the SAT and ACT. Students learn the basics of setting up and solving these ratios and working on application problems including angle of elevation and angle of depression problems. This unit also paces the students through learning the concepts and stops to review with mixed types of problems so students learn problem solving techniques. Both simplifying radicals with special right triangles and using the calculator to solve trig equations are addressed in the unit.  
Each lesson has a video and corresponding note-taking guide, as well as a practice worksheet that corresponds to each lesson. Each lesson covers one main concept with direct instruction and appropriate independent practice problems. The worksheets are clean and easy to copy for students.

Description of the video and note-taking guides:

Lesson 1
  • Review of the characteristics of a triangle
  • Introduction to the Pythagorean Theorem
  • Works several sample problems involving using the Pythagorean Theorem in order to find missing sides of a triangle
  • Find the area of an isosceles triangle that has a base of 12 and two sides measuring 10.
  • Gives directions on solving Pythagorean Theorem word problems
  • This lesson covers simplifying radical expressions. The video works nine of these problems

Lesson 2
  • Working with the 30 60 90 Special Right Triangle
  • Looking at the patterns of a 30 60 90 special right triangle
  • Given the short leg how do you find the long leg and the hypotenuse?
  • Given the long leg of a 30 60 90 triangle, find the short leg and the hypotenuse.
Lesson 3
  • Working with 45 45 90 special right triangles
  • Looking at the special patterns of a 45 45 90 triangle
  • Given a leg of a 45 45 90 triangle find the hypotenuse
  • This lesson works many examples of finding the leg length or the hypotenuse of a 45 45 90 triangle
  • Find the area of a square given the diagonal. The diagonal divides the square into two 45 45 90 triangles which can be used to find the area of the square.

Lesson 4 (no video)
Review of Lesson 1-3 with mixed types of problems.

Lesson 5
  • Explanation of the ratios for sine, cosine, and tangent
  • Step by step instructions.  
  •  Label the angle
  •  Label the sides, 
  •  What do you know, 
  •  Write the ratio, 
     •    Solve
  • Solving multiple examples of these trig ratios, using cross multiplying
  • Using your calculator to evaluate trig values and solve these equations.
​Lesson 6
  • Using your calculator to evaluate angles
  • Working the trig functions backward to find missing angles given two sides
  • Step by step instructions
  •  Decide which sides you have from the reference angle,
  •  Decide your trig function, set up,
  •  Solve using the 2nd function keys
  • Several practice problems including angle of elevation and angle of depression
Lesson 7
  • Cumulative trig review with mixed practice problems using the three trig ratios
  • Working problems to solve for sides and inverse problems involving solving for angles
Lesson 8
  • Trig word problems involving all the concepts from the unit.
Lesson 9 (no video)
  • Trigonometry Vocabulary