hard trigo..plz help?

Question

4. Express the following in radians:

a.135°c. 60°e. -150°
b.- 15°d. 112.5°f. °1025



5. Express the following in degrees, minutes, and seconds:

A. 4
B. 0.23
C. π/6
D. 3π/2
E. – 1.4
F.9.6



6. What is the size, in degrees, of the angle subtended by an arc of 1 2/3 ft in a circle whose radius is 45 in.?

Answer 1

Just use the conversion factors
(180°/π rad) = 1
and
(π rad/180°) = 1.

Therefore
4)
a.
135°
= 135° · (1)
= 135° · (π rad/180°)
= 3π/4 rad

b.
-15°
= -15° (1)
= -15° (π rad/180°)
= -π/12 rad

c.
60°
= 60° (π rad/180°)
= π/3 rad

d.
112.5°
= 112.5° (π rad/180°)
= 5π/8 rad

e.
-150°
= -150° (π rad/180°)
= -5π/6 rad

f.
1025°
= 1025° (π rad/180°)
= 205π/36 rad

__________________
5)
A.
4 rad
= 4 rad (1)
= 4 rad(180°/π rad)
= (720/π)°
= 229° 10' 59.22"

B.
0.23 rad
= 0.23 rad (180°/π rad)
= 13° 10' 40.91"

C.
π/6 rad
= π/6 rad (180°/π rad)
= 60°

D.
3π/2 rad
= 3π/2 rad (180°/π rad)
= 270°

E.
-1.4 rad
= -1.4 rad (180°/π rad)
= -80° 12' 50.73"

F.
9.6 rad
= 9.6 rad (180°/π rad)
= 550° 2' 22.14"

_________________________
6. The formula for the angle θ (measured in radians) subtending an arc with length s in a circle with radius of r is:
θ = s/r

To make them have the same unit, convert the feet. We now have:
s = 1 2/3 ft = 20 in. and r = 45 in.

Therefore,
θ = s/r = 20 in/45 in

Therefore,
θ = 4/9 rad

Convert it into degrees
θ = 4/9 rad (1)
θ = 4/9 rad (180°/π rad)
θ = (80/π)°
θ = 25° 27' 53.25"

Therefore, the angle is 25° 27' 53.25".
^_^

Answer 2

There are 180 degrees in pi radians. So:

To convert from degrees to radians multiply by: pi/180

To convert from radians to degrees multiply by: 180/pi

Answer 3

I like it when you post the number of the homework problem you're looking for the answer to.

Answer 4

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