Pg. 323/361 Homework Pg. 362 #39 – 47 odd, 51, 52 Memorize Trig. Info #2QIV#4QIII#6QIII #8-250°#10470° #12338°, 698°, -382°, -742°#14210°, 570°, -510°,

Slides:

Advertisements

Similar presentations

Trigonometry/Precalculus ( R )

Advertisements

7.3 Trigonometric Functions of Angles. Angle in Standard Position Distance r from ( x, y ) to origin always (+) r ( x, y ) x y  y x.

Drill Calculate:.

Section 7-4 Evaluating and Graphing Sine and Cosine Objectives: To use the reference angles, calculators and tables and special angles to find the values.

Special Right Triangles

Solving Right Triangles

Definition of Trigonometric Functions With trigonometric ratios of acute angles in triangles, we are limited to angles between 0 and 90 degrees. We now.

Finding Exact Values of Trig Ratios. Special Right Triangles

13.3 Trigonometric Functions of General Angles

7.3 Special Angles (30  & 60  ). Equilateral Triangle 60  angles w/ sides = 1 Drop Perpendicular Bisector to form  1 60   60  30.

7.3 Special Angles (45 & Quadrantal)

5.1 Angles and Radian Measure. ANGLES Ray – only one endpoint Angle – formed by two rays with a common endpoint Vertex – the common endpoint of an angle’s.

The Pythagorean Theorem. The Right Triangle A right triangle is a triangle that contains one right angle. A right angle is 90 o Right Angle.

4.2 Trigonometric Function: The Unit circle. The Unit Circle A circle with radius of 1 Equation x 2 + y 2 = 1.

SPECIAL USING TRIANGLES Computing the Values of Trig Functions of Acute Angles.

0.2: Trignometric Functions Objective: Understand relationships between angles and sides of right triangles Review trig functions of special & quadrantal.

1 Trigonometry Basic Calculations of Angles and Sides of Right Triangles.

7.2 Right Triangle Trigonometry. A triangle in which one angle is a right angle is called a right triangle. The side opposite the right angle is called.

Warm Up Use Pythagorean theorem to solve for x

Pg. 324 Homework Memorize familiar radian measure angles Pg. 323#2 – 52 even Pg. 361#1 – 13 all.

13.2 – Define General Angles and Use Radian Measure.

30º 60º 1 45º 1 30º 60º 1 Do Now: Find the lengths of the legs of each triangle.

Chapter 4 Trigonometric Functions Trig Functions of Any Angle Objectives:  Evaluate trigonometric functions of any angle.  Use reference angles.

Pg. 324 Homework Memorize familiar radian measure angles Pg. 361#1 – 13 all #1QIII#3QII#5QI #7408° #9345° #11415°, 775°, -305°, -665° #1350°, 770°, -510°,

4.3 Right Triangle Trigonometry

Section 6.1 Notes Special Angles of the Unit Circle in degrees and radians.

3.6 Functions of Special & Quadrantal Angles. The key  DRAW THE ANGLE & TRIANGLE!! Quadrantal angle = angle with terminal side on x- or y-axis Ex 1)

5.3 The Unit Circle. A circle with center at (0, 0) and radius 1 is called a unit circle. The equation of this circle would be So points on this circle.

Pg. 362 Homework Pg. 362#56 – 60 Pg. 335#29 – 44, 49, 50 Memorize all identities and angles, etc!! #40

Pg. 352 Homework Study, Study, Study!! **Test Wednesday!!** #15#36-120°, -2π/3 #2368°, 112°#4723°, 23π/180 = 0.40 #5175°#290.36, 0.93, 0.38 #371.28, 1.27,

Find all 6 trig ratios from the given information sinθ = 8/133. cotθ = 5   9 15.

4.4 Pythagorean Theorem and the Distance Formula Textbook pg 192.

Objectives: 1.To find trig values of an angle given any point on the terminal side of an angle 2.To find the acute reference angle of any angle.

4.4 – Trigonometric Functions of any angle. What can we infer?? *We remember that from circles anyway right??? So for any angle….

Pythagorean Theorem Converse Special Triangles. Pythagorean Theorem What do you remember? Right Triangles Hypotenuse – longest side Legs – two shorter.

4.2 Trig Functions of Acute Angles. Trig Functions Adjacent Opposite Hypotenuse A B C Sine (θ) = sin = Cosine (θ ) = cos = Tangent (θ) = tan = Cosecant.

Pre-AP Pre-Calculus Chapter 4, Section 3 Trigonometry Extended: The Circular Functions

13.1 Right Triangle Trigonometry. Trigonometry: The study of the properties of triangles and trigonometric functions and their applications. Trigonometric.

6.1 – 6.5 Review!! Graph the following. State the important information. y = -3csc (2x) y = -cos (x + π/2) Solve for the following: sin x = 0.32 on [0,

Objective: Use unit circle to define trigonometric functions. Even and odd trig functions. Warm up 1.Find and. 2.Give the center and radius of a circle.

Trigonometric Function: The Unit circle Trigonometric Function: The Unit circle SHS Spring 2014.

5.2 Trigonometric Ratios in Right Triangles. A triangle in which one angle is a right angle is called a right triangle. The side opposite the right angle.

§5.3.  I can use the definitions of trigonometric functions of any angle.  I can use the signs of the trigonometric functions.  I can find the reference.

Two Special Right Triangles

Pythagorean Theorem and it’s Converse

6.3 Trig Functions of Angles

Special Right Triangles

7-6 Sine and Cosine of Trigonometry

Solving Right Triangles

4.2 Trigonometric Function: The Unit circle

Trigonometric Function: The Unit circle

Trig Functions and Acute Angles

Help I’m trapped in a nutshell

THE UNIT CIRCLE.

7.7 Solve Right Triangles Obj: Students will be able to use trig ratios and their inverses to solve right triangles.

THE UNIT CIRCLE.

Unit 7 – Right Triangle Trig

TRIGONOMETRIC FUNCTIONS OF ANY ANGLE

Section 3 – Trig Functions on the Unit Circle

Lesson 7.7, For use with pages

Warm – Up: 2/4 Convert from radians to degrees.

Trigonometric Function: The Unit circle

Trigonometric Functions of Any Angle (Section 4-4)

Unit 7B Review.

4.2 Trigonometric Function: The Unit circle

Warm-up: Find the exact values of the other 5 trigonometric functions given sin= 3 2 with 0 <  < 90 CW: Right Triangle Trig.

4.4 Trig Functions of any Angle

1.3 – Trigonometric Functions

θ hypotenuse adjacent opposite θ hypotenuse opposite adjacent

Agenda Go over homework

Presentation transcript:

Pg. 323/361 Homework Pg. 362 #39 – 47 odd, 51, 52 Memorize Trig. Info #2QIV#4QIII#6QIII #8-250°#10470° #12338°, 698°, -382°, -742°#14210°, 570°, -510°, -870° #1611π/4, -5π/2#1829π/6, -19π/6 #20π/4, 9π/4, -15π/4, -23π/4#2267°, 157° #2478°, 168°#265π/12, 11π/12#28π/14, 4π/7 #3090°, π/2#32135°, 3π/4#340°, 0, 2π #36-120°, -2π/3#38-600°, -10π/3# °, -7π #42π/3#447π/6#4611π/6 #4859π/90#50249π/180#52810/π #1#2#38/7 #47/8#5#6 #7 #811/15#9#10 #11#12#1315/11

6.5 Trig Functions of an Acute Angle Trig Functions The six trig functions of any angle 0° < Ɵ < 90° are defined as follows: Also, we know that from the basic three trig functions:

6.5 Trig Functions of an Acute Angle Example: They hypotenuse and one leg of a triangle measure 12 and 7 respectively. Find the measure of angle Ɵ formed by these two sides. Let Ɵ be an acute angle such that sin Ɵ = 5/6. Find all the trig functions of Ɵ. One angle of a right triangle measures 38°, and the hypotenuse has length of 17. Find the measures of the remaining sides.

6.5 Trig Functions of an Acute Angle Example: Find the values of the six trig functions at an angle Ɵ in standard form with point P(4, 7) on its terminal side. **Note** If an angle does not appear acute in the first quadrant, you can work in any of the four quadrants to make the angle acute!! Find the values of all six trig functions and the angle of measure of angle Ɵ, where P(-3, 4) is a point on the terminal side of Ɵ. Find all the values of all six trig functions for the quadrantal angles of:

6.5 Trig Functions of an Acute Angle Determining Ɵ Given the following, find the measure of Ɵ in both degrees and radians.

6.5 Trig Functions of an Acute Angle Proving. Can you prove that 65+2 = 75 – 3 How do you know this? Prove that: