Trigonometry

Question 1

Find angles between 0 and 360 degrees which are the same as -Π/2, 1180^oand 9Π/4

Answer 1

1. The first is negative so we add 2Π.
   
   1. -Π/2 + 2Π = 3Π/2
2. 1180^o = 1180⁰ - 360⁰ = 820⁰ = 460⁰ = 100^o
3. 9Π/4 radians = 9 Π/4 - 2Π radians= Π/4 radians

Question 2

How do we find the CosΘ and sinΘ are for arbitrary Θ ?

Answer 2

1. Determine the quadrant.
2. Draw right triangle by drawing an altitude to the the x axis.
3. Get the Cartesian co-ordinates (x,y).
4. Points to the left of the y axis have a negative * x* and those below have a negative y.
5. we then set sin Θ = x
6. and cos Θ = y

Question 3

Find tan 7π/4

Answer 3

1. Determine quadrant – since 7π/4 is greater than 3π/2 and less than 2π, the angle is in the fourth quadrant.
2. Draw altitude.
3. Determine the acute angle which is: π/4
4. cos π/4 = sqrt(2)/2 as is sin π/4.
5. Determine sign: since the angle is in the fourth quadrant and x is positive and y is negative, so cos 7π/4 is positive and sin 7π/4 is negative.
6. tan 7π/4 = (sin 7π/4 )/ (cos 7π/4) = -1

Question 4

Qadrants: 30, 700, 5π/3 and - 3π/5

Answer 4

1. 30: Quadrant 1
2. 700 : Q IV
3. 5π/3 : Q IV
4. • 3π/5: Q III

Question 5

sin(30 )

Answer 5

1/2

Question 6

sin(45)

Answer 6

sqrt(2) /2

Question 7

sin 60

Answer 7

sqrt(3) / 2

Question 8

sin 90

Answer 8

1

Question 9

sin 120

Answer 9

sqrt(3) / 2

Question 10

sin 135

Answer 10

sqrt(2) / 2

Question 11

sin 150

Answer 11

1/2

Question 12

sin 180

Answer 12

0

Question 13

sin 210

Answer 13

• 1/2

Question 14

sin 225

Answer 14

-sqrt(2) / 2

Question 15

sin 240

Answer 15

• sqrt (3) / 2

Question 16

sin 270

Answer 16

-1

Question 17

sin 300

Answer 17

• sqrt(3) / 2

Question 18

sin 315

Answer 18

• sqrt(2) / 2

Question 19

sin 330

Answer 19

• 1/2

Question 20

sin 360

Answer 20

= sin 0 = 0

Question 21

cos 0

Answer 21

1

Question 22

cos 30

Answer 22

sqrt(3) / 2

Question 23

cos 45

Answer 23

sqrt(2) / 2

Question 24

cos (60)

Answer 24

1/2

Question 25

cos 90

Answer 25

0

Question 26

cos 120

Answer 26

• 1/2

Question 27

cos 135

Answer 27

• sqrt(2) / 2

Question 28

cos 150

Answer 28

• sqrt(3) / 2

Question 29

cos 180

Answer 29

-1

Question 30

cos 210

Answer 30

• sqrt(3) / 2

Question 31

cos (225)

Answer 31

• sqrt(2) / 2

Question 32

cos(240)

Answer 32

• 1 /2

Question 33

cos 270

Answer 33

0

Question 34

cos 300

Answer 34

1/2

Question 35

cos 315

Answer 35

sqrt(2) / 2

Question 36

cos (330)

Answer 36

sqrt(3) / 2

Question 37

cos 360

Answer 37

= cos 0 = 1

Question 38

pi/6 radians

Answer 38

30 degrees

Question 39

pi/3 radians

Answer 39

60 degrees

Question 40

π / 4 radians

Answer 40

45^o

Question 41

π / 2 radians

Answer 41

90^o

Question 42

2 π/3

Answer 42

120 degrees

Question 43

Determine sin 300

Answer 43

Quadrant ==> IV

• sqrt(3) / 2

Question 44

csc 150

Answer 44

1 / sin

==> 1 / (sin 150)

== 1 / sin(30)

== 2

Question 45

cot 5π/3

Answer 45

Quadrant IV

cot(-π/3)

cot (- π/3)

• sqrt(3) / 3

cos(π/3) = 1/2

cot(π/3) [=] 1/3sqrt(3)

csc(π/3) = 2/3sqrt(3)
(7)
[sec(pi/3)] [=] [2]
(8)
[sin(pi/3)] [=] [1/2sqrt(3)]
(9)
[tan(pi/3)] [=] [sqrt(3).]

Question 46

signs of cos theta

and sin thetha

given theta?

Answer 46

cos is positive in I,IV, negative in II, III

sin is positive in I, II, negative in III, IV

Question 47

find sin(105)

Answer 47

What is the exact value of sin(105º)?

We can use a sum angle formula noticing that 105º = 45º + 60º.

We have sin(105º) = sin(45º + 60º) = sin(45º )cos(60º) + cos(45º )sin(60º).

We know the exact values of trig functions for 60º and 45º.

Therefore, sin(45º )cos(60º) + cos(45º )sin(60º)

(sqrt(2) + sqrt(6))/4