We think you have liked this presentation. If you wish to download it, please recommend it to your friends in any social system. Share buttons are a little bit lower. Thank you!
Presentation is loading. Please wait.
Published byMolly Ramsey
Modified over 2 years ago
Ch 5.5: Multiple-Angle and Product-to-Sum Formulas
Double Angle Formulas Half Angle Formulas The + or – depends in which quadrant the original given value exists
Ex: Find the sin2Ө and cos2Ө if 1. Draw a triangle 2. Find the missing piece 3. Use the formula
Ex: Find the triple angle formula for: 1. Rewrite the inside as a sum 2. Use the formula from Replace with double angle formulas 4. Pythagorean Identity 5. Simplify
Ex: Use the half angle formula to find the exact value of sin(105 o ) 2. Double 105 to get the numerator 3. Plug into the half formula exists in the II, so sine is positive! Simplify
Product-to-Sum and Sum-to-Product formulas: Ex: Use the correct formula to write the following product as a sum or difference: 1. Change using formula 2. Simplify
Ex: Find the exact value of 1.Change using sum-to- product formula 2. Simplify 3. Use trig to change cosines 4. Simplify
VerifyTriangles Sum/Difference Formulas Half Angle, Product to Sum, Sum to Product FINAL JEOPARDY.
Using Fundamental Identities Objectives: 1.Recognize and write the fundamental trigonometric identities 2.Use the fundamental trigonometric identities.
13.3 T RIG FUNCTIONS OF GENERAL ANGLES Algebra II w/ trig.
Chapter 7 Review. Solve for 0° ≤ θ ≤ 90° 1.) If tan θ = 2, find cot θ2.) if sin θ = ⅔, find cos θ 3.) If cos θ = ¼, find tan θ4.) If tan θ = 3, find sec.
Determining signs of Trig Functions (Pos/Neg) x y Last class we found trig values using an x-y coordinate. Not all trig values are positive We can determine.
Section 5.4 – Properties of Logarithms. Simplify:
DegRad DegRad DegRad. x y Find the for all angles that are between 0 and 360 degrees (also in include the radian measurements From the chart we get that.
By bithun jith. Done by bithun jith binoy k.v.pattom You must know and memorize the following. Pythagorean Identities: sin 2 x + cos 2 x = tan 2.
X y Find the exact trig values for an angle of This angle has a terminal side in the 2 nd quadrant (because 5/4 = 1.2)
By: Linitha and Hina. 7.1 Exploring Equivalent Trigonometric Functions Related functions with and 2 Cos ( – θ)= - cos θ Sin ( – θ) = sin θ Tan ( – θ)
Trigonometric Equations In quadratic form, using identities or linear in sine and cosine.
Proving the Distance Formula. What is the distance between points A and B? We can use the Pythagorean Theorem to find the distance.
Trigonometry Review. Hopefully, you remember these from last year (you were required to memorize ten of them) plus SOH CAH TOA. If not, you need to.
Warm UpJan. 24 th Graph the following: 1.f(x) = -2 + sin3x 2.g(x) = 2cos(x – ) + 1.
Slide 6-1 Equations 6.1 Solving Trigonometric Equations 6.2 More on Trigonometric Equations 6.3 Trigonometric Equations Involving Multiples Angles 6.4.
Trigonometry Ratios. Example 1 Write the Trig Ratio for each of the following ( soh, cah, toa)
(x, y) r Use Pythagorean Theorem: x 2 + y 2 = r 2 Note: x can be and y can be (depending on the Quadrant) Since r is the radius, it must be (+) because.
1.1 The Cartesian Plane Ex. 1 Shifting Points in the Plane Shift the triangle three units to the right and two units up. What are the three.
Section 2.3 – Product and Quotient Rules and Higher- Order Derivatives.
Circular Trigonometric Functions Y X r θ circle…center at (0,0) radius r…vector with length/direction angle θ… determines direction.
Finding Reference Angles. It is necessary to be able to make larger angles smaller. We do this by finding reference angles: Step: 1.Start by drawing the.
Polar Coordinates We Live on a Sphere. Polar Coordinates Up till now, we have graphed on the Cartesian plane using rectangular coordinates In the rectangular.
Resultant of two forces Resultant of parallel forces Resultant of perpendicular forces Resultant two forces at any angle Learning objectives.
Mathematics. Session Properties of Triangle - 2 Session Objectives.
2.4 Writing the Equation of a Line. Review of Slope-Intercept Form The slope-intercept form of a linear equation is y = mx + b. m represents the slope.
Write equations and graph circles in the coordinate plane. Objectives.
CH 8 Right Triangles. Geometric Mean of 2 #’s If you are given two numbers a and b you can find the geometric mean. a # = # b 3 x = x 27 Ex ) 3 and 27.
CHAPTER 4 Trigonometric Functions. 4.1 Angles & Radian Measure Objectives –Recognize & use the vocabulary of angles –Use degree measure –Use radian measure.
Copyright © Cengage Learning. All rights reserved. 4.3 Right Triangle Trigonometry.
VECTORS IN A PLANE Pre-Calculus Section 6.3. CA content standards: Trigonometry 12.0 Students use trigonometry to determine unknown sides or angles in.
© 2016 SlidePlayer.com Inc. All rights reserved.