Find three angles, two positive and one negative, that are coterminal with the g

Question

Find three angles, two positive and one negative, that are coterminal with the given angle: 7??18
a)-11??18,43??18,79??18
b)-25??18,25??18,43??18
c)-11??18,25??18,43??18
d)-29??18,43??18,79??18
e)-29??18,25??18,79??18
Review Later Find three angles, two positive and one negative, that are coterminal with the given angle: 7??18
a)-11??18,43??18,79??18
b)-25??18,25??18,43??18
c)-11??18,25??18,43??18
d)-29??18,43??18,79??18
e)-29??18,25??18,79??18
Review Later Question 2 Name the quadrant in which the given conditions are satisfied: tan(?) > 0 ,csc(?) < 0
a)IV
b)II
c)I
d)III
Review Later Question 2 Name the quadrant in which the given conditions are satisfied: tan(?) > 0 ,csc(?) < 0
a)IV
b)II
c)I
d)III
Review Later Question 3 Let P(x,y) denote the point where the terminal side of an angle?meets the unit circle. IfPis in Quadrant II andy=3?4, evaluate the six trigonometric functions of?.

Review Later Question 4 Rewrite the following expression in terms of its reference angle, deciding on the appropriate sign (positive or negative): csc(300 Question 4 Rewrite the following expression in terms of its reference angle, deciding on the appropriate sign (positive or negative): csc(300

Explanation / Answer

For coterminal angles difference between angles should be 2pi or multiple of 2pi

1) d)-29??18,43??18,79??18

since(-29pi/18)-7pi/18- = -2pi(negative)

(43pi/18)-7pi/18- = 2pi(positive)

(79pi/18)-7pi/18- = 4pi(positive)

2)Third quadrant tan is positve and cosec is negative

3)Since y = 3/4

x^2 = 1^2 - (3/4)^2 = 7/16 (Since it is a unit circle)

x = - Sqrt(7)/4 (since it is in second quadrant)

Cos(theta) = x/1 =- Sqrt(7)/4

sin(theta) = y/1 = 3/4 (In second quadrant sin is positive)

hence e

4) cosec(theta) = -cosec(360-theta) when 180<theta<360

hence e

5)sec(theta) = -sec(180-theta) when 90<theta<180

hence b

6) -6pi is the x axis hence point is (1,0) tan(2n*pi) = 0

cosec(2n*pi) = undefined

hence d

7) Sin-1(-sqrt(3)/2) = -pi/3

since sin(-pi/3) = sqrt(3)/2

hence c

8)Cos-1(1/2) = pi/3

since cos(pi/3)= 1/2

hence b

9) tan-1(sqrt(3)) = pi/3

since tan(pi/3) = sqrt(3)

hence d

10) sin-1(-sqrt(2)) = undefined

since the domain is either less than -1 or greater than 1

hence c

11)c (since it repeats after a minimum period of pi)

12)d since the diffence b/w highest and lowest/2 = 1

13)b

since period of sin(nx) = 2pi/n

14)a

since amplitude of a*cos(x)= a

15)b

since cos(-(pi-nx)) = -cos(nx) and period of cos(nx )is 2pi/n

3*2pi/pi= 6

16)e

since for asinx-b amplitude is (a-b)-(-a-b)/2 = a

hence 8

17)a

the phase shift is pi to right as for cos(x-a) phase shift is a rightwards

18) d since the graph shifts 3 units downwards as for acos(x)+b shift is b upwards

19)d since the amplitude is 3 in acos(x)+b a should be 3 and since it shifted 1 unit downward b is -1

20)csince the amplitude is 2 in asin(x)+b a should be 2 and since it shifted 1 unit upward b is 1

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