4.4 Day 1 Trigonometric Functions of Any Angle –Use the definitions of trigonometric functions of any angle –Use the signs of the trigonometric functions Pg. 499 #2-22 (even)

At any point on the circle, we can connect a vertical line to the x-axis and create a triangle. Horizontal side = x, vertical side=y, and hypotenuse=r. x and y may be positive or negative (depending on their direction) The radius, r, is always a positive value. For any point (x,y) found on the circle, sin Θ = y cos Θ = x = Reciprocal of Sine = Reciprocal of Cosine

Given a point (-3,-4), find the 6 trig. functions associated with the angle formed by the ray containing this point. x=-3, y=-4, and so r = Then, sin A = -4/5, cos A = -3/5, tan A = 4/3 csc A = -5/4, sec A = -5/3, cot A = ¾ Since, sin A = y/r, cos A = x/r, tan A = y/x csc A = r/y, sec A = r/x, cot A =x/y

1.Let P = (1, -3) be a point on the terminal side of Θ. Find each of the six trigonometric functions of Θ.

Evaluate, if possible, the cosine function at the following four quadrant angles: 2.0 o o o o

Evaluate, if possible, the cosecant function at the following four quadrant angles: 6. 0 o o o o

Here’s a helpful anagram to help you remember the signs (positive or negative) of trigonometric functions: All Snowflakes Taste Cold All functions Sine and cosecant Tangent and cotangent Cosine and secant are (+) in are (+) in Quadrant I Quadrant II Quadrant III Quadrant IV Another way to think of the sign of a function is to remember the variable it is defined by. Since the radius is always positive, only the signs of x and y influence the sign of the function. In any given quadrant: cosine and secant have the same sign as x sine and cosecant have the same sign as y tangent and cotangent have the same sign as the ratio of x and y

Determine the quadrant in which angle Θ lies. 10. sin Θ sin Θ sec Θ > 0 and cot Θ < tan Θ < 0 and csc Θ < 0