Sec 2.1 Trigonometric Functions

of Acute Angles

October 1, 2012

Warm – Up (10/1) 

   

B

A C

(x,y)

y (opposite side)

r

x(adjacent side)

hypotenuse

Right Triangle w/ Respect to Angle A

Right Triangle Based Definitions of Trigonometric FunctionsFor any acute angle A in standard position,

 

 

 

Right Triangle Based Definitions of Trigonometric FunctionsFor any acute angle A in standard position,

 

 

 

I Do It

Find the values of the six trigonometric functions for angle A.

14

19

23

A

We Do It TogetherFind the values of the six trigonometric functions for angle A.

4652

22A

CofunctionsFind the values of the six trigonometric functions for angle A and B.

4652

22A

Conclusions:

Cofunctions

 

 

 

B

C A

a

b

c

The sum of the three angles in any triangle is ____.

Angle B and angle A are ____________ angles. (Since angle C = 90°, the sum of angle A + angle B = 180°- 90° = ____.

Reviewing Facts about Right Triangle

Since angles A and B are: complementary & sinA = cosB (A + B = 90°)

The functions sine and cosine are called

COFUNCTIONS!

Cofunctions

Since

90BA&

sinA = cosB

Thus… 

Cofunction IdentitiesFor any acute angle A, since

 

 

 

Cofunction IdentitiesFor any acute angle A, since

 

 

 

Cofunction IdentitiesFor any acute angle A, since

 

 

 

I Do ItWrite the following in terms of its cofunctions.

 

 

We Do It TogetherWrite the following in terms of its cofunctions.

 

 

You Do It Together

Write the following in terms of its cofunctions.

 

 

Homework

Pg. 68 #7, 9, 11, 13, 15,17, 19, 21

Warm – Up (10/2)

Write the following in terms of its cofunctions.

 

 

 

Since angles A and B are: complementary & sinA = cosB (A + B = 90°)

The functions sine and cosine are called

COFUNCTIONS!

Cofunctions

I Do It

Find a value of θ satisfying each equation. Assume that all angles involved are acute angles.

 

We Do It Together

Find a value of θ satisfying each equation. Assume that all angles involved are acute angles.

 

You Do It TogetherFind a value of θ satisfying each equation. Assume that all angles involved are acute angles. 

Comparing Function Values of Special Angles

r

A A

r

A

r

Conclusion:As A increases, y increases. Since r is fixed, sinA increases.

r

A

yA

ry

A

r y

 

Conclusion:As A increases, x decreases. Since r is fixed, cosA decreases.

r

A xA

r

x

A

r

x

 

Conclusion:As A increases, y increases and x decreases. Since r is fixed, tanA increases.

r

A x

A

r y

x

 

A

r

x

yy

I Do ItTell whether each statement is true or false.

 

TRUE

We Do It TogetherTell whether each statement is true or false.

 

FALSE

You Do It TogetherTell whether each statement is true or false.

 

TRUE

You Do It TogetherTell whether each statement is true or false.

 

FALSE

Homework (10/2)

Pg. 69 # 23 – 33 odds

Warm – Up (10/3)Tell whether each statement is true or false. 

 

 

Trigonometric Function Values of Special Angles

30°- 60°- 90° Triangle:

30°

60°

1

60°

30° 1

 

x

1

1

60°

1

 

30° 

Trigonometric Function Values of 30°-60°-90° Angles

For 30° angle:

Hypotenuse =Side Opposite =Side Adjacent =

 

 

 

 

 

 

30°

60°

Trigonometric Function Values of 30°-60°-90° Angles

For 60° angle:

Hypotenuse =Side Opposite =Side Adjacent =

 

 

 

 

 

 

1

 

30° 

Trigonometric Function Values of 45°-45°-90° Angles

45°

45°

x

x

1

For 45° angle:

Hypotenuse =Side Opposite =Side Adjacent =

 

 

 

 

 

 

Function Values of Special Angles

θ sinθ cosθ

tanθ

cotθ

secθ

cscθ

30°

45°

60°

I Do ItGive the exact trigonometric function value. 

 

  

We Do It TogetherGive the exact trigonometric function value.

A line makes a 30° angle with the x – axis and crosses through the origin. What is the equation of the line?

We Do It Together

You Do It TogetherA line makes a 45° angle with the x – axis and crosses through the origin. What is the equation of the line?

 

We Do It Together

 

You Do It Together