1. 7.5 The Other Trigonometric Functions

2. 7.5 T HE O THER T RIG F UNCTIONS Objectives:  Evaluate csc, sec and cot Vocabulary: Cosecant, Secant, Cotangent

3. Right Triangle Trig. Functions

4. If is a second quadrant angle and sin is 3/5, find the remaining five functions. 7.5 T HE O THER T RIG F UNCTIONS

5. Find the six trig functions for: 330° 7.5 T HE O THER T RIG F UNCTIONS

6. x Find the six trig functions of 330 o. Second, find the reference angle, 360 o – 330 o = 30 o [Solution] First draw the 330 o angle. To compute the trig functions of the 30 o angle, draw the “special” triangle or recall from the table. Determine the correct sign for the trig functions of 330 o. Only the cosine and the secant are “+”. A S TC 330 o 30 o

7. [Solution] The six trig functions of 330 o are: Find the six trig functions of 330 o.

8. 7.5 T HE O THER T RIG F UNCTIONS

9. A S TC Find the six trig functions of. y x Before we write the functions, we need to determine the signs for each function. Remember “All Students Take Calculus”. Since the angle,, is located in the 3 rd quadrant, only the tangent and cotangent are positive. All the other functions are negative..

10. 7.5 T HE O THER T RIG F UNCTIONS

11. 0 radians Find the six trig functions for. We will first draw the angle to determine the quadrant. A S TC We know that is the same as 45, so the reference angle is 45. Using the special triangle. Note that the reference angle is. We see that the angle is located in the 3rd quadrant.

12. 7.5 T HE O THER T RIG F UNCTIONS

15. TB p. 286#13-27 odd 7.5 T HE O THER T RIG F UNCTIONS

16. Since the sine function is periodic with a fundamental period of 360 o or 2 , the graph above can be extended left and right as show below.

17. The Cosecant Graph Vertical Asymptote:  = k , where k  Z cot and csc have the same Vertical Asymptote:  = k , where k  Z

18. To graph the cosine function, we analyze the x coordinate of the rotating particle in a similar manner, since the cosine function has the fundamental period of 360 o or 2 , the graph above can be extended left and right as show below:

19. From graphs below, we find 1.sine graph and cosine graph have the same shape. 2.each one is the horizontal transformation to the other. 3.sine graph is symmetry to the origin and therefore it is an odd function. sin(–  )= – sin  4.cosine graph is symmetry to the y-axis and therefore it is an even function. cos(–  )= cos  5.sin  = cos(  –  /2) or sin  = cos(  – 90 o ) 6.cos  = sin(  +  /2) or cos  = sin(  + 90 o )

20. The Secant Graph

21. Vertical Asymptote:  = k  +  /2, where k  Z tan and sec have the same Vertical Asymptote:  = k  +  /2, where k  Z

22. The Tangent Graph Vertical Asymptote:  = k  +  /2, where k  Z

23. The Cotangent Graph TANGENT COTANGENT

24. TB p. 285#7-9, 11, 12, 22 19 and 21 if not finished last night. 7.5 T HE O THER T RIG F UNCTIONS