1. Warm UP Graph arcsin(x) and the limited version of sin(x) and give their t-charts, domain, and range

2. Math IV Lesson 36 Essential Question: What are the inverse trig functions, and How can I use them to simplify trigonometric Equations?

6. Standard(s): Standards: MM4A8. Students will investigate and use inverse sine, inverse cosine, and inverse tangent functions. a. Find values of the above functions using technology as appropriate. b. Determine characteristics of the above functions and their graphs.

7. Review Graph arccos(x) and the limited version of cos(x) and give me their domain and Range

8. Review Graph the limited version of tan(x) and arctan(x) and give me the domain and range

11. Quiz: Graph the following and give the domain and range 1.limited version of sin(x) 2.Graph arcsin(x) 3.limited version of cos(x) 4.Graph arccos(x) 5.limited version of tan(x) 6.Graph arctan(x) Bonus - arccos( -1) =

12. Introduction to solving Trigonometric equations Your preliminary goal in solving a trigonometric equation is to isolate the trigonometric function in the equation. To solve a trigonometric equation, use standard algebraic techniques such as collecting like terms and factoring. For example, to solve the equation 2 sin x = 1, divide each side by 2 to obtain

13. How many solutions are there to trig equations ….. well how many times can you go around the unit circle? However, We will be talking about solving trig equations on the interval from [0,2 ㅠ ]

14. Methods to solving equations Finding the angles that make the statement true. Several methods for solving these types of equations that are similar to methods used with polynomials. – Combining like terms – Taking square roots – Factoring

15. remember cos(Ө) = x, sin(Ө) = y and tan(Ө) = y/x Using the unit circle to get exact values, solve for x, [0, 2π): 1. cos x = ½ 2. sin x = 0 3. tan x = ± √ 3 4. cos x = -1

16. Many times you will have to manipulate the equation to solve 1. Combining like terms 2. Using identities to simplify 3. Factoring

17. Try these: Solve for x: 0 = 4x – 2 0 = 4sin x – 2

18. Now try these: Solve for x: 0 = 2x 2 + 3x + 1 0 = 2cos 2 x + 3cos x + 1

19. 4sin 2 x – 3 = 0 sin x – cos x sin x = 0 sin x (sec 2 x + 1) = 0 2sin 2 x = 2 + cos x

20. A Few Rules: 1.Look for values on the unit circle 2.When taking the square root, don’t forget the + and – 3.Never divide by a variable, move to the other side of the equation and factor! Given 3tan 3 x = tan x Subtract tan from both sides 3tan 3 x – tan x = 0 Factor tan x(3tan 2 x – 1) = 0 Solve: tan x = 0 or 3tan 2 x – 1 = 0 tan 2 x = 1/3