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 Functions For any acute angle A in standard position,

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

I Do It Find the values of the six trigonometric functions for angle A A

We Do It Together Find the values of the six trigonometric functions for angle A A

Cofunctions Find the values of the six trigonometric functions for angle A and B A

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 & sinA = cosB Thus…

Cofunction Identities For any acute angle A, since

Cofunction Identities For any acute angle A, since

Cofunction Identities For any acute angle A, since

I Do It Write the following in terms of its cofunctions.

We Do It Together Write 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 Together Find 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 y A r y A r y

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

I Do It Tell whether each statement is true or false. TRUE

We Do It Together Tell whether each statement is true or false. FALSE

You Do It Together Tell whether each statement is true or false. TRUE

You Do It Together Tell 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°60° 1 60°60° 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° x x 1 For 45° angle: Hypotenuse = Side Opposite = Side Adjacent =

Function Values of Special Angles θ sin θ cos θ tan θ cot θ sec θ csc θ 30° 45° 60°

I Do It Give the exact trigonometric function value.

We Do It Together Give 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 Together A 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