Trigonometry/Pre-Calculus 4.4 Any Angle Trig

Trig 11/22/2018 Give the values of the trig functions. 1. 4. 2. 5. 227 HW: p284 1-7 odd, 13-25 odds, 29-61 odds,67-71 odds Honors: ILO 4, 12-28 all, 29-65 odds, 67-73 odds, 91-94 Give the values of the trig functions. 1. 4. 2. 5. 3. 6. Today’s Lesson: Any Angle Trigonometry

Google Form 4.3c #1 and 2 You are standing 65 meters from the base of the Jin Mao Building in Shanghai, China. You estimate that the angle of elevation to top of the 88th floor is 80o. What is the approximate height of the building (rounded to whole meters)? One of your friends is on the 88th floor. What is the distance between you and your friend (rounded to whole meters)?

Trig of Right Triangles A 12-m flagpole casts a 12-m shadow, as shown in the figure. Find x, the angle of the elevation to the sun. x

Trig/Pre-Calculus Today’s Lesson: 4.4a Any Angle Trigonometry You will: Evaluate trig functions of any angle. Use reference angles to evaluate trig functions

Signs and Quadrants signs all sin tan cos

Which Quadrant? State the quadrant in which theta lies.

Which Quadrant? State the quadrant in which theta lies.

Which Quadrant? State the quadrant in which theta lies.

Trig Functions of Any Angle Reference Angle, 𝜃′ is the acute angle 0≤𝜃≤90° formed by the terminal side and the x-axis. (x,y)

Reference Angle Drawing a reference angle, .

Reference Angle Drawing a reference angle, .

Reference Angle Drawing a reference angle, .

Reference Angle Drawing a reference angle, .

Reference Angle Drawing a reference angle, .

Reference Angles Reference angle, ’, is measured from the x-axis.

Reference Angles Reference angle, ’, is measured from the x-axis.

Reference Angles Reference angle, ’, is measured from the x-axis.

Reference Angles Reference angle, ’, is measured from the x-axis.

Reference Angles Reference angle, ’, is measured from the x-axis.

Reference Angles For = 30o, what is the reference angle?

Reference Angles For = 132o, what is the reference angle?

Reference Angles For , what is the reference angle?

Reference Angles For , what is the reference angle?

Reference Angles For , what is the reference angle?

Reference Angles Find the reference angles ’.

Reference Angles Find the reference angles ’.

Reference Angles Find the reference angles ’.

Reference Angles Find the reference angles ’. 1.57 3.14

Reference Angles Find the reference angles ’. 180o 135o

Reference Angles Find the reference angles ’.

Reference Angles Find the reference angles ’.

Reference Angles Find the reference angles ’.

Evaluate each trigonometric function.

Evaluate each trigonometric function.

Evaluate each trigonometric function.

Evaluating Trig Functions Let (–3,4) be a point on the terminal side of . Find the sine, cosine, and tangent of . (-3,4) r

Evaluating Trig Functions Given the and , Find and -t +c -t 4 +c -5