Exact Values of angles in trig?

Question

How do u work out the exact angles of these trigonometry questions? They are in my test 2mrw and i dnt know how to do it. Here are some practice questions i received from my teacher:
Find exact values of:
a) tan 60 degrees
b) cos (pi)/4
c) sin -45 degrees

and how do u solve these equations:

0 a) cos theta= -0.5
b)sin theta= -0.5

please show working out.

Answer 1

Question 1
a)
sides of triangle are 1 , √3 , 2
tan 60° = √3 / 1 = √3

b)
sides of triangle are 1 , 1 , √2
cos (π / 4) = 1 / √2

c)
sides of triangle are 1, 1, √2
- 45° is in 4th quadrant
sin (- 45°) = - (1 / √2)

Question 2
a)
cos θ = - 0.5
θ = 120° , θ = 240°

b)
sin θ = - 0.5
θ = 210° , θ = 330°

Answer 2

You must be talking about the unit circle and the sine and cosine values. It is important because all of the classes that follows trig you are taking uses that value. It will help you alone the way if you know them by heart. Besides.... if you remember 4 values in quadrant 1, then remember the signs and which goes which (sine and cosine), you can expand this knowledge to the entire unit circle. It's not that hard.

Answer 3

Do you have a scientific calculator?
a)tan 60=3^1/2
b) not sure
c)sin -45= -sin45= -1/(2^1/2)

a)inverse cos -0.5=basic angle
there will be 2 answers:
1) 180-basic angle
2) 180+basic angle

b)inverse sin -0.5=basic angle
there will be 2 answers:
1)180+basic angle
2)360-basic angle

hope this helps. :)

Answer 4

a)tan 60=3^1/2
b) not sure
c)sin -45= -sin45= -1/(2^1/2)

a)inverse cos -0.5=basic angle
there will be 2 answers:
1) 180-basic angle
2) 180+basic angle

b)inverse sin -0.5=basic angle
there will be 2 answers:
1)180+basic angle
2)360-basic angle

Answer 5

a) . . . tan 60 = sqr(3)
b) . . . . cos( pi/4) = 1/sqr(2) = sqr(2) /2
c) . . . sin -45 = - sqr(2) /2

a) . . . cos A = - 0.50
A = 180 + 60 = 240 . . . and . .. A = 180 - 60 = 120 deg

b) . . . . sin A = - 0.50
A = 180 +30 = 210 deg . . . and . . . A = 360 - 30 = 330 deg

Answer 6

memorize these formulas
sin(90-A)=cos(A)
tan(90-A)=cot(A)
sec(90-A)=csec(A)
sin60=cos30=sqrt(3)/2
sin30=cos60=1/2
sin45=cos45=sqrt(2)/2

a) tan 60 degrees=sin60/cos 60=(sqrt(3)/2)/(1/2)=sqrt(3)
b) cos (pi)/4=sqrt(2)/2
c) sin -45 degrees=sin(315)=-sqrt(2)/2
-1<=Cos theta<=1
-1<=SIn theta<=1
a) cos theta= -0.5; theta=60 degrees
b)sin theta= -0.5 ,theta=-30 degrees

Answer 7

you can find the value in trigonometric table at the back of your textbook.