Trigonometry Review Find sin(  /4) = cos(  /4) = tan(  /4) = Find sin(  /4) = cos(  /4) = tan(  /4) = csc(  /4) = sec(  /4) = cot(  /4) = csc(

Slides:



Advertisements
Similar presentations
Example Express -8sinx° + 15cosx° in the form ksin(x + )° *********
Advertisements

Trigonometry Review Find sin(  /4) = cos(  /4) = tan(  /4) = Find sin(  /4) = cos(  /4) = tan(  /4) = csc(  /4) = sec(  /4) = cot(  /4) = csc(
If k(x) =f (g(x)), then k’(x) = f ’ ( g(x) ) g’(x) k(x) = sin( x 2 ) k’(x) = cos ( x 2 ) 2x.
Graphs of Other Trigonometric Functions
The Inverse Trigonometric Functions Section 4.2. Objectives Find the exact value of expressions involving the inverse sine, cosine, and tangent functions.
Write the following trigonometric expression in terms of sine and cosine, and then simplify: sin x cot x Select the correct answer:
Extra 5 pt pass if…. You can find the exact value of cos 75˚ with out a calculator. Good luck!!
Chapter 7: Trigonometric Identities and Equations
By: Kelley Borgard Block 4A
Tips For Learning Trig Rules. Reciprocal Rules Learn:
Product and Quotient Rules and Higher – Order Derivatives
If is measured in radian Then: If is measured in radian Then: and: -
Trigonometric Identities
Warm Up: h(x) is a composite function of f(x) and g(x). Find f(x) and g(x)
Right Triangle Trigonometry
Chapter 6 Trig 1060.
Cofunction Identities
6.2: Right angle trigonometry
 Content  What is derivation?  Derivation of trigonometry function  Derivation’s rules.
If k(x) =f (g(x)), then k’(x) = f ’ ( g(x) ) g’(x) k(x) = sin( x 2 ) k’(x) = cos ( x 2 ) 2x.
Antiderivative. Buttons on your calculator have a second button Square root of 100 is 10 because Square root of 100 is 10 because 10 square is
Derivatives. What is a derivative? Mathematically, it is the slope of the tangent line at a given pt. Scientifically, it is the instantaneous velocity.
Warm Up Determine the derivative of each of the following.
Using our work from the last few weeks,
Copyright © 2011 Pearson, Inc Fundamental Identities Goal: Use the fundamental identities to simplify trigonometric expressions.
Graphs of the Trig Functions Objective To use the graphs of the trigonometric functions.
Trigonometry Review Find sin(  /4) = cos(  /4) = tan(  /4) = Find sin(  /4) = cos(  /4) = tan(  /4) = csc(  /4) = sec(  /4) = cot(  /4) = csc(
Unit 4: Trigonometry Minds On. Unit 4: Trigonometry Minds On AngleSinCosTan.
Trig Review. 1.Sketch the graph of f(x) = e x. 2.Sketch the graph of g(x) = ln x.
B.1.8 – Derivatives of Primary Trig Functions Calculus - Santowski 12/1/ Calculus - Santowski.
Lesson 5-3b Fundamental Theorem of Calculus. Quiz Homework Problem: ( 3e x + 7sec 2 x) dx Reading questions: Fill in the squares below f(x) dx = F(█)
 The derivative of a function f(x), denoted f’(x) is the slope of a tangent line to a curve at any given point.  Or the slope of a curve at any given.
Lesson 39 - Derivatives of Primary Trigonometric Functions IB Math HL - Santowski 12/14/2015Calculus - Santowski1.
Ch. 4 – More Derivatives 4.1 – Chain Rule. Ex: Find the derivative of h(x) = sin(2x 2 ). –This is not a product rule problem because it has one function.
SEC 8.2: TRIGONOMETRIC INTEGRALS
Find the critical point of f(x) =(2x - 1) on [0,  ] A. x = ½ B. x = 1 C. x = 2 D. x = 3.
Practice Evaluate each of the following.
Some needed trig identities: Trig Derivatives Graph y 1 = sin x and y 2 = nderiv (sin x) What do you notice?
EXAMPLE 1 Evaluate trigonometric functions given a point Let (–4, 3) be a point on the terminal side of an angle θ in standard position. Evaluate the six.
Dean Bates P derivatives of trig functions.
Trigonometry Review Find sin(  /4) = cos(  /4) = tan(  /4) = Find sin(  /4) = cos(  /4) = tan(  /4) = csc(  /4) = sec(  /4) = cot(  /4) = csc(
Describe the vertical shift in the graph of y = -2sin3x + 4. A.) Up 2 B.) Down 2 C.) Up 4 D.) Down 4.
BELL-WORK TCAP Bell-Work # What is the cotangent of angle x if sec(x) = 12 5.
Power Rule is a corallary to Chain Rule. Power Rule If f(x) = x n then f ' (x) = n x (n-1) Replacing x by g(x) gives.
Trigonometric Identity Review. Trigonometry Identities Reciprocal Identities sin θ = cos θ = tan θ = Quotient Identities Tan θ = cot θ =
CHAPTER Continuity Fundamental Theorem of Calculus In this lecture you will learn the most important relation between derivatives and areas (definite.
Section 4.2 The Unit Circle. Has a radius of 1 Center at the origin Defined by the equations: a) b)
Meet the Parents Interception Who’s Line is It anyway?
4.3 Right Triangle Trigonometry Objective: In this lesson you will learn how to evaluate trigonometric functions of acute angles and how to use the fundamental.
Pythagorean Identities Unit 5F Day 2. Do Now Simplify the trigonometric expression: cot θ sin θ.
Jeopardy Simplify Trig expressions Verify Trig Identities Find all Solutions Solutions with multiple angles Solutions with factoring Q $100 Q $200 Q $300.
Math 1304 Calculus I 3.2 – Derivatives of Trigonometric Functions.
Warm Up 1)Evaluate: arccos (- ½ ) 2)Write an algebraic expression for tan (arcsin (5x)). 3) Given f(x) = x 3 + 2x – 1 contains the point (1, 2). If g(x)
The Unit Circle and Circular Functions Trigonometry Section 3.3.
Warm Up Determine the average rate of change of
Inverse Trigonometric Functions
Simplifying Trig. Identities
Review 5.1 to 5.3.
Lesson 6.5/9.1 Identities & Proofs
Trig Functions: the unit circle approach
Part (a) 1 1 ax ax ax 2 g(x) = e + f(x) g’(x) = e (ln e) (a) + f’(x)
One way to use identities is to simplify expressions involving trigonometric functions. Often a good strategy for doing this is to write all trig functions.
Last time… Homework questions?.
Using Fundamental Identities
Trig. equations with graphs
Copyright © Cengage Learning. All rights reserved.
Part (a) h(1) = f(g(1)) - 6 h(3) = f(g(3)) - 6 h(1) = f(2) - 6
Math /4.4 – Graphs of the Secant, Cosecant, Tangent, and Cotangent Functions.
Main Ideas of Hon PreCalc Ch. 5 Class 1
Quick Integral Speed Quiz.
Presentation transcript:

Trigonometry Review Find sin(  /4) = cos(  /4) = tan(  /4) = Find sin(  /4) = cos(  /4) = tan(  /4) = csc(  /4) = sec(  /4) = cot(  /4) = csc(  /4) = sec(  /4) = cot(  /4) =

Evaluate tan(  /4) A. Root 2 B. 2 C. Root 2 /2 D. 2 / Root 2 E. 1

Trigonometry Review sin(2  /3) = cos(2  /3) = tan(2  /3) = sin(2  /3) = cos(2  /3) = tan(2  /3) = csc(2  /3) = sec(2  /3) = cot(2  /3) = csc(2  /3) = sec(2  /3) = cot(2  /3) =

Evaluate sec(2  /3) A. -1 B. -2 C. -3 D. Root(3) E. 2 / Root(3)

Evaluate cos(  /2) A. -1 B C. 1 D. 0.0

Evaluate sin(  /3) A B. 0.5 C D

If y = sec(  ), find y if  =

Squeeze Theorem If f(x) g(x) h(x) on an open interval containing a, and then

Rule 4 is a Theorem

Theorem -> Sector Area = x/2 Theorem -> Sector Area = x/2

Proof.. ½ sin(x)cos(x) ½ x ½ sin(x)/cos(x) ½ sin(x)cos(x) ½ x ½ sin(x)/cos(x) cos(x) x/sin(x) 1/cos(x) cos(x) x/sin(x) 1/cos(x) 1 1 therefore 1 therefore 1

sin(.1)= sin(.01)= sin(.001= sin(.0001)= sin( )=

Rule 5 is a Theorem = 0 Proof cos(A+B)=cos(A)cos(B)-sin(A)sin(B) If A = B = x/2 cos(x)= 1 -

2sin 2 (x/2)= 1-cos(x)

= 0

Equation of Lines Write the equation of a line that passes through (-3, 1) with a slope of – ½.

Equation of Lines Write the equation of a line that passes through (-3, 1) with a slope of – ½.

Equation of Lines Write the equation of a line that passes through (-3, 1) with a slope of – ½.

Equation of Lines Write the equation of a line that passes through (-3, 1) with a slope of – ½.

Passes through (0,1) with a slope of -3. What is the missing blue number?

Write the equation of the line tangent to y = x + sin(x) when x = 0 given the slope there is 2. A. y = 2x + 1 B. y = 2x C. y = 2x

Write the equation of the line tangent to y = x + sin(x) when x = 0 given the slope there is 2. A. y = 2x + 1 B. y = 2x C. y = 2x