BY: MARIAH & JON 13.4 INVERSE OF SINE AND TANGENT.

Slides:



Advertisements
Similar presentations
Trigonometric Equations
Advertisements

Section 7.1 The Inverse Sine, Cosine, and Tangent Functions.
7-4 Evaluating Trigonometric Functions of Any Angle Evaluate trigonometric functions of any angle Use reference angles to evaluate trigonometric functions.
Section 7.2 The Inverse Trigonometric Functions (Continued)
EXAMPLE 1 Evaluate inverse trigonometric functions Evaluate the expression in both radians and degrees. a.cos –1 3 2 √ SOLUTION a. When 0 θ π or 0° 180°,
Trigonometric Equations Section 5.5. Objectives Solve trigonometric equations.
Taking a Square Root to Solve an Equation. Solve: In order to solve for x, you have to UNDO the squared first (i.e. square root) What are the number(s)
Finding Exact Values For Trigonometry Functions (Then Using those Values to Evaluate Trigonometry functions and Solve Trigonometry Equations)
8.5 Solving More Difficult Trig Equations
Maths revision course by Miriam Hanks
Essential Question: What are the restricted domains for the sin, cos, and tan functions?
EXAMPLE 1 Use an inverse tangent to find an angle measure
Inverses  How do we know if something has an inverse? ○ Vertical line tests tell us if something is a function ○ Horizontal line tests will tell us if.
Solving Equations Containing To solve an equation with a radical expression, you need to isolate the variable on one side of the equation. Factored out.
Copyright © 2005 Pearson Education, Inc.. Chapter 6 Inverse Circular Functions and Trigonometric Equations.
DegRad        DegRad      DegRad    
Sum and Difference Formulas New Identities. Cosine Formulas.
Copyright © 2005 Pearson Education, Inc.. Chapter 6 Inverse Circular Functions and Trigonometric Equations.
Section 6.4 Inverse Trigonometric Functions & Right Triangles
Trigonometric Equations M 140 Precalculus V. J. Motto.
Lesson 4.2. A circle with center at (0, 0) and radius 1 is called a unit circle. The equation of this circle would be (1,0) (0,1) (0,-1) (-1,0)
Slide Copyright © 2007 Pearson Education, Inc. Publishing as Pearson Addison-Wesley.
1 © 2010 Pearson Education, Inc. All rights reserved © 2010 Pearson Education, Inc. All rights reserved Chapter 4 Trigonometric Functions.
WHAT ARE SPECIAL RIGHT TRIANGLES? HOW DO I FIND VALUES FOR SIN, COS, TAN ON THE UNIT CIRCLE WITHOUT USING MY CALCULATOR? Exact Values for Sin, Cos, and.
Inverse Trigonometric Functions 4.7
4.7 INVERSE TRIGONOMETRIC FUNCTIONS. For an inverse to exist the function MUST be one- to - one A function is one-to- one if for every x there is exactly.
Trig Functions of Angles Right Triangle Ratios (5.2)(1)
13.7 I NVERSE T RIGONOMETRIC F UNCTIONS Algebra II w/ trig.
4.7 Inverse Trig Functions. By the end of today, we will learn about….. Inverse Sine Function Inverse Cosine and Tangent Functions Composing Trigonometric.
The Unit Circle M 140 Precalculus V. J. Motto. Remembering the “special” right triangles from geometry. The first one is formed by drawing the diagonal.
And because we are dealing with the unit circle here, we can say that for this special case, Remember:
1 8.1 Inverse Trigonometric Functions In this section, we will study the following topics: Definitions of the inverse trig functions Evaluating inverse.
Values of the Trig Functions Reference angles and inverse functions (5.4)
Inverse Trig Functions Objective: Evaluate the Inverse Trig Functions.
Sin, Cos, Tan with a calculator  If you are finding the sin, cos, tan of an angle that is not a special case (30, 60, 45) you can use your calculator.
Finding Trigonometric Function Values using a Calculator Objective: Evaluate trigonometric functions using a calculator.
1 © 2011 Pearson Education, Inc. All rights reserved 1 © 2010 Pearson Education, Inc. All rights reserved © 2011 Pearson Education, Inc. All rights reserved.
By: Clay Pennington Wade Davis Perri Lyles Cara Sbrissa.
Simple Trigonometric Equations The sine graph below illustrates that there are many solutions to the trigonometric equation sin x = 0.5.
Warm Up. 8-1 Simple Trigonometric Equations Objective: To solve simple Trigonometric Equations and apply them.
Standard 20 The Quadratic Formula Example with numbers put in.
The Inverse Trigonometric Functions. Let's again review a few things about inverse functions. To have an inverse function, a function must be one-to-one.
Notes 2.1 and 2.2 LOOKING FOR SQUARES AND SQUARE ROOTS.
Sketching Angles and Reference Angles Sketch an angle of 275º and then find its reference angle x y The angle is a little more than that 270º so it is.
Section 8-1 Simple Trigonometric Equations. Solving Trigonometric Equations The sine graph (on p. 295) illustrates that there are many solutions to the.
T2.1 e To Find the Inverse Functions for sin Ө, cos Ө, tan Ө cot Ө, sec Ө, & csc Ө “It’s an obstacle illusion” –Alan-Edward Warren, Sr Got.
Use Reference Angles to Evaluate Functions For Dummies.
Inverse Trig Functions. If cos (x) = 0 then what is x?
LESSON 10-1: THE PYTHAGOREAN THEOREM. SIMPLIFYING RADICALS LESSON 10-2.
8-3 Trigonometry Part 2: Inverse Trigonometric Functions.
Section 4.4 Trigonometric Functions of Any Angle.
Reviewing Trigonometry Angle Measure Quadrant Express as a function of a positive acute angle Evaluate Find the angle Mixed Problems.
C H. 4 – T RIGONOMETRIC F UNCTIONS 4.7 – Inverse Trig Functions.
Section 4.7 Inverse Trigonometric Functions. Helpful things to remember. If no horizontal line intersects the graph of a function more than once, the.
February 13 th copyright2009merrydavidson. Inverse functions switch the x and y values. The inverse is NOT a function. y = arcsin x y = sin -1 x 4.7Inverse.
EXAMPLE 1 Use an inverse tangent to find an angle measure Use a calculator to approximate the measure of A to the nearest tenth of a degree. SOLUTION Because.
Warm Up. Reference Angles If you know the reference angle, use these formulas to find the other quadrant angles that have the same reference angle Degrees.
Trigonometric Functions
The Inverse Sine, Cosine and Tangent Functions
Solving Equations Containing
Solving Equations Containing
Trigonometric Equations with Multiple Angles
1B.1- Solving Quadratics:
Solving Equations Containing
THE UNIT CIRCLE.
THE UNIT CIRCLE.
Solving Division Equations
Geometry Section 7.7.
Solving Equations Containing
Warm Up Change to radians ° ° ° °
Presentation transcript:

BY: MARIAH & JON 13.4 INVERSE OF SINE AND TANGENT

INVERSE SINE Say that the sine of theta equals A. To find the inverse sine you would put that sine to the -1 of whatever A equals would then equal theta. A can not be less than -1 or greater than 1.

EXAMPLE A now equals -1. Inverse the equation so sine of theta now equals A or now -1. Look at your chart if it’s a special angle! If so find what degree the sine of 1 equals. Since A is negative, theta will also be negative. Also once you find the angle convert it to radians as well. If its not a special angle use your calculator.

LET’S PRACTICE

ANSWER

INVERSE TANGENT Inverse tangent works the same as inverse sine. Say that the tangent of theta equals A. The inverse tangent of A would then equal theta A can be anything because it ranges from negative infinity to positive infinity. Your answer, or theta, is the same ranges for inverse sine.

EXAMPLE A now equals the square root of 3 over 3. Inverse the equation so the tan of theta now equals A, or now the square root of 3 over 3. Again look at your chart to see if it’s a special angle! Put your answer in degrees and radians and don’t forget to see if it’s negative. If not special use a calculator!

LET’S PRACTICE

ANSWER