Presentation is loading. Please wait.

Presentation is loading. Please wait.

Unit Circle ( √3, 1 ) 2 2 ( 1, √3 ) 2 2 ( √2, √2 ) 2 2 30˚ 45˚ 60˚

Published byNoel Underwood Modified over 8 years ago

Similar presentations

Presentation on theme: "Unit Circle ( √3, 1 ) 2 2 ( 1, √3 ) 2 2 ( √2, √2 ) 2 2 30˚ 45˚ 60˚"— Presentation transcript:

1 Unit Circle ( √3, 1 ) 2 2 ( 1, √3 ) 2 2 ( √2, √2 ) 2 2 30˚ 45˚ 60˚

2 Use the Unit Circle to find cos 135 Reference angle: 45 Coordinate: x Sign: - Answer: -√2 2

3 Use the Unit Circle to find sin 315 Reference angle: 45 Coordinate: y Sign: - Answer: -√2 2

4 Use the Unit Circle to find sin 180 Reference angle: none Coordinate: y Sign: N/A Answer: 0

5 Use the Unit Circle to find cos 210 Reference angle: 30 Coordinate: x Sign: - Answer: -√3 2

6 Use the Unit Circle to find tan 225 Reference angle: 45 Coordinate: y/x Sign: -/- = + Answer: 1

7 Use the Unit Circle to find sin 120 Reference angle: 60 Coordinate: y Sign: + Answer: √3 2

8 Use the Unit Circle to find cos 120 Reference angle: 60 Coordinate: x Sign: - Answer: -1 2

9 Use the Unit Circle to find tan 270 Reference angle: none Coordinate: y/x Sign: N/A Answer: 1 = undefined 0

10 Use the Unit Circle to find tan 360 Reference angle: none Coordinate: y/x Sign: N/A Answer: 0 = 0 1

11 Use the Unit Circle to find cos 90 Reference angle: none Coordinate: x Sign: N/A Answer: 0

12 Use the Unit Circle to find cos 150 Reference angle: 30 Coordinate: x Sign: - Answer: -√3 2

13 Use the Unit Circle to find cos 330 Reference angle: 30 Coordinate: x Sign: + Answer: √3 2

14 Use the Unit Circle to find cos 240 Reference angle: 60 Coordinate: x Sign: - Answer: -1 2

15 Use the Unit Circle to find tan 180 Reference angle: none Coordinate: y/x Sign: N/A Answer: 0 = 0 1

16 Use the Unit Circle to find tan 135 Reference angle: 45 Coordinate: y/x Sign: +/- = - Answer: -1

17 Use the Unit Circle to find tan 135 Reference angle: 45 Coordinate: y/x Sign: +/- = - Answer: -1

Download ppt "Unit Circle ( √3, 1 ) 2 2 ( 1, √3 ) 2 2 ( √2, √2 ) 2 2 30˚ 45˚ 60˚"

Similar presentations

Determining signs of Trig Functions (Pos/Neg)

Determining signs of Trig Functions (Pos/Neg)
Finding Reference Angles

Finding Reference Angles
SOHCAHTOA TOA CAH SOH The three trigonometric ratios for right angled triangles are considered here. Click on a box to select a ratio.

SOHCAHTOA TOA CAH SOH The three trigonometric ratios for right angled triangles are considered here. Click on a box to select a ratio.
ET-314 Week 11 Nov 7, 2014 Topic(s): 19.1 Vectors.

ET-314 Week 11 Nov 7, 2014 Topic(s): 19.1 Vectors.
Trigonometry Right Angled Triangle. Hypotenuse [H]

Trigonometry Right Angled Triangle. Hypotenuse [H]
Trig Graphs. y = sin x y = cos x y = tan x y = sin x + 2.

Trig Graphs. y = sin x y = cos x y = tan x y = sin x + 2.
1 Special Angle Values. 2 Directions A slide will appear showing a trig function with a special angle. Work out the answer Hit the down arrow to check.

1 Special Angle Values. 2 Directions A slide will appear showing a trig function with a special angle. Work out the answer Hit the down arrow to check.
1 Special Angle Values. 2 Directions A slide will appear showing a trig function with a special angle. Work out the answer Hit the down arrow to check.

1 Special Angle Values. 2 Directions A slide will appear showing a trig function with a special angle. Work out the answer Hit the down arrow to check.
1 Special Angle Values DEGREES. 2 Directions A slide will appear showing a trig function with a special angle. Say the value aloud before the computer.

1 Special Angle Values DEGREES. 2 Directions A slide will appear showing a trig function with a special angle. Say the value aloud before the computer.
Review 6.1-6.4.

Review
1.5 Using the Definitions of the Trigonometric Functions OBJ: Give the signs of the six trigonometric functions for a given angle OBJ: Identify the quadrant.

1.5 Using the Definitions of the Trigonometric Functions OBJ: Give the signs of the six trigonometric functions for a given angle OBJ: Identify the quadrant.
Signs of functions in each quadrant. Page 4 III III IV To determine sign (pos or neg), just pick angle in quadrant and determine sign. Now do Quadrants.

Signs of functions in each quadrant. Page 4 III III IV To determine sign (pos or neg), just pick angle in quadrant and determine sign. Now do Quadrants.
TRIGONOMETRY. Sign for sin , cos  and tan  Quadrant I 0° <  < 90° Quadrant II 90 ° <  < 180° Quadrant III 180° <  < 270° Quadrant IV 270 ° < 

TRIGONOMETRY. Sign for sin , cos  and tan  Quadrant I 0° <  < 90° Quadrant II 90 ° <  < 180° Quadrant III 180° <  < 270° Quadrant IV 270 ° < 
Section 7.2 The Inverse Trigonometric Functions (Continued)

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°,

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 Functions on the

Trigonometric Functions on the
Pre calculus Problem of the Day Homework: p. 472 1-17 odds, 25-31 odds, 39-59 odds On the unit circle name all indicated angles by their first positive.

Pre calculus Problem of the Day Homework: p odds, odds, odds On the unit circle name all indicated angles by their first positive.
Find the period of the function y = 4 sin x. 1234567891011121314151617181920 2122232425262728293031323334353637383940 41424344454647484950 1. 2. 3.

Find the period of the function y = 4 sin x
UNIT CIRCLE. Review: Unit Circle – a circle drawn around the origin, with radius 1.

UNIT CIRCLE. Review: Unit Circle – a circle drawn around the origin, with radius 1.
Using Trigonometric Ratios

Using Trigonometric Ratios

Similar presentations

Ads by Google