Section 7 5 The Other Trigonometric Functions Objective

Section 7 -5 The Other Trigonometric Functions Objective: To find the values of: the tangent, cotangent, secant, and cosecant functions and to sketch the functions’ graphs.

FILL IN THE TABLE BELOW Quadrant I II IV

Topics to know for today’s lesson n n

We can define other trig functions in terms of (x, y). name Abbreviation tangent of tan cotangent of cot secant of sec cosecant of csc definition

Reciprocals

Fill in the table below with appropriate signs Q 1 tan cot sec csc Q 2 Q 3 Q 4

Fill in the table below with appropriate signs Q 1 Q 2 Q 3 Q 4 tan + - cot + - sec + - - + csc + + - - Positive Negative

Find the value of each; round to the nearest hunderdths n HINT: Make sure to use the proper mode.

Function Restrictions Definition restriction

Why do the restrictions matter The value of the function on the calculator n The graph of the function. n

Find the value of each expression to four significant digits. A. ) tan 203° B. ) cot 165° C. ) csc (-1) D. ) sec 11

Express each in terms of reference angle: n

Sec 7. 5 day 2 Express each of the following in terms of a reference angle. n

Tangent and secant functions on unit circle.

Cotangent and cosecant on the unit circle

n

n

If was in degrees: How would each graph be different? n How would each graph be the same? n What would the period and amplitude be? n

Given θ is a second-quadrant angle n

Homework written exercise sec 7. 5 n DAY 1: # 1 -9 all n DAY 2: #10 -19 all and 23 - 27 odds Optional: Check out: Graphing program online: Desmos Or http: //www. padowan. dk/