UNIT 4 – INTRODUCTION TO TRIGONOMETRY NAME: _______________________________ PRE-CALCULUS HONORS WARMUP – FILL IN THE FOLLOWING INFORMATION TO THE BEST OF YOUR ABILITY.

• A Unit Circle is a circle with a radius of ______ unit and is centered at the _________. The Unit Circle includes the coordinates and angle measures (in both ______________ and _____________) at several key points around the circle. There are several applications and uses for the Unit Circle, which we will explore ☺

• We can convert from Degrees to Radians by multiplying by __________________.

• We can convert from Radians to Degrees by multiplying by __________________.

• We read the Unit Circle _______________________________ for positive angle measurements and ____________________ for negative angle measurements.

• Coterminal Angles are angles that share the same __________________ and __________________ sides. Every angle has an __________________ amount of coterminal angles.

• Reference Angles are the ____________ angle (from the ___________ quadrant) formed by the _____________ and the ______________________ side of an angle. Example: 30° is the reference angle for _____, ______, and ______.

• We can rationalize denominators, such as <√>

, by ___________________________________________________.

• Arc Length Formula: ______________________________________

• Pythagorean Theorem Formula (used for Right Triangles): _________________________________________

• SOH-CAH-TOA means sin(x)=__________, cos(x)=___________, and tan(x)=____________.

• Fill in the values for the missing sides of the following special triangles:

1 1

Honors Pre-Calculus Name:____________________________________ Review of Trig Day 1 (Chapter 4 Section 1) TRIGON: METRON: I. REVIEWING SINE AND COSINE GRAPHS

Use your knowledge of basic transformations to graph the following (LABEL THE AXES appropriately): 1) 2sin −= xy 2) xy sin3−=

3) 3cos += xy 4) xy cos4= 5) xy cos−= 6) 1sin2 += xy

II. REVIEW OF THE UNIT CIRCLE

Last year, we explored the idea of finding heights and distances along the edge of a Ferris Wheel and looked specifically at a wheel with a radius of 1. We found out that when the radius = 1:

sine represents ____________________________________. cosine represents __________________________________.

If we were to plot the Ferris Wheel on a set of x- and y- axes, we would know all of the coordinates of the points shown. Fill in all degree values, radian values, heights, and displacements:

** The values for Quadrant I need to be committed to memory (for life… not crammed). There will be multiple quizzes on this beginning next class. Recall SohCahToa?

sin B =

cos B =

hypotenuse

adjacent

opposite θ

tan B =

III. Arc Length Review

Recall: A central angle measures 1 Radian when the arc length = the radius. So what changes if the arc length is 0.5r? Or 2r? Write a formula for arc length using s for arc length, ɵ for the radian measure of the angle, and r for radius.

Suppose you are trying to find the area of the sector (shaded region).

B = FGH

and I = 4. Find the area, leaving your answer exact.

Explore using other values for theta and r, leaving your answer for area exact. For example, what changes if B = G

J?

What if r = 8? Take your findings and develop an area formula for sectors.