Question

Instruction: Find the exact value of each of the following. That is, no decimals are allowed, and no calculators are allowed. In each case, show your work and explain the steps you take to find the value.

(Given) Part 1: Sin 17pi/6
Q 1. Use the fact that there are 2pi radians in each circle to find another angle, smaller than 2pi, that is equivalent to 17pi/6.
Q 2. Find the sine of the angle you found in part 1. This is also 17pi/6.


(Given) Part2: tan. 13pi/4
Q1. Use the fact that there are 2pi radians in each circle to find another angle, smaller than 2pi that is equivalent to 13pi/4.
Q2. Find the tangent of the angle you found in part 1. This is also 13pi/4.


Given Part 3: sec. 11pi/3
Q1. Use the fact that there are 2 pi radians in each circle to find another angle, smaller than 2pi, this is equivalent to 11pi/3.
Q2. Find the secant of the angle you found in Par1. This is also 11pi/3.

Answer 1

Answer:

Part 1.

1. pi/6

2. 0.5

Part 2.

1. 5pi/4

2. 1.

Part 3.

1. 5pi/3

2. 2.

Step-by-step explanation:

1. 17pi/6 - 2pi = 5pi/6

5p/6 is in the second quadrant where the sine is  positive and sine 5pi/5 is equivalent to sin pi/6.

the required angle is pi/6.

2. From the unit circle we see that  sin pi/6 = 0.5.

Part 2.

1. 13pi/4 - 2pi = 5pi/4

2. This is in the third quadrant where the tangent is positive.

tan 5pi/4 = tan pi/4 = 1.

Part 3.

1. 11pi/3 - 2pi = 5pi/3

2. Sec = 1/ cos

so sec 5pi/3 = 1 / cos 5pi/3.

2pi - 5pi/3 = pi/3

cos pi/3 = 0.5

sec pi/3 = 1/0.5 = 2.