Know the definition of reference angles and how to find the

Know the definition of reference angles and how to find the reference angle from a given theta theta = 5pi/4 theta = -160 degree Know which functions are positive and negative in the different quadrants. Know your reciprocals and the ratio of each trig function (i.e sin theta = y/r) Find the values of the six trigonometric functions of theta with the given constraint. Function value Constraint csc theta = 4 cot theta 0, find sine and secant. Evaluate sine, cosine, and tangent functions of the real number. t = 2pi/3 theta = -3pi/4 Evaluate the trigonometric function as well as the inverse function (refer to coral handout). tan(-210 degree) cot(pi) sin330 degree sec 3pi/4 sin^-1(- Squareroot 2/2) Determine the exact values of the trig functions given that the point on the terminal side is (-8, 15) Know how to sketch function and find the amplitude, period, and intervals y = -3sin 10x y = -co 2x/3 y = 2 cos(6x + pi) y = sin x/2 - 1 Know how to solve application problems that involve right triangles, (looking for the missing angle) An engineer build a 75-foot cellular telephone tower. Find the angle of elevation to the top of the tower at a point on level ground 50 ft. from the its base.

Solution

1) A reference angle is an angle formed by the x axis and the terminal side. For any given angle we need to see the angle formed by its terminal side with axis to find the reference angle.

a) theta = 5pi/4   = pi +pi/4 . So, pi/4

b) theta = -160 = -180 +20 . So, +20 deg

2) Q -I : All are +ve

Q2 : sin --+ve , cos -- -ve ; tan --- -ve

Q3 : sin ---> -ve , cos ---- -ve , tan--- +ve

Q4 : sin ---> -ve ; cos---> +ve , tan --- -ve

sintheta = y/r ; cscstheta = r/y

costheta = x/r ; sectheta = r/x

tantheta = y/x ; cottheta = x/y