3.5 The Trig Functions

sine cosine cosecant secant tangent cotangent sine and cosine are only 2 of the trig functions! Here are all 6!, x ≠ 0, y ≠ 0

Ex 1) The terminal side of an angle θ in standard position passes through (–1, 7). Draw the reference triangle and evaluate the six trig functions of θ. –1 7 r θ (–1) 2 = r 2 50 = r 2  r always (+)

Ex 2) Determine the value of secθ if cosθ = 0.11 A relationship among the 6 trig functions is they can pair up & make pairs of reciprocal functions. (as always den ≠ 0)

If we know the value of one trig function & the quadrant of θ, we can get the other 5 Ex 3) Angle in standard position, Quadrant IV and –6 7 θ x

Ex 4) Suppose that cos θ = 0.42 and Use the symmetry of the unit circle to find the exact values of the following. a) cos(–θ) θ –θ–θ x-value is the same so cos(–θ) = 0.42 b) cos(θ + π) θ + π x-value is negative so cos(θ + π) = –0.42 c) cos(θ + 2π) θ + 2π right where you started so cos(θ + 2π) = 0.42

Homework #305 Pg 150 #1, 5, 9, 13, 15, 17, 21, 26, 27, 29, 31, 33, 37, 43, 44, 45, 46