Plane Trig 3 help??

Question

1. Using exact values, fine the numerical value of :
a. sin 30* cos 240* + sin 210* sin 300*
b. tan 225* + tan (-45*)

2. Express each of the following as the same function of a positive acute angle:
a. cos 112* 33'
b. tan 310*
c. cot 138* 15' 10"
d. sin (-140*)

3. Express eash as a function of 0:
a. sin (270* + 0)
b. tan 310*
c. tan (810* + 0)
d. sin (0-180*)

4. find the value of:
a. log sin 62* 22' 33"
b. log cot 28* 13' 17"
c. log cos 125* 15' 23"
d. log tan 78* 45' 50"

5. find the acute angle A, to the nearest second when:
a. log cos A = 9.12575
b. log sin A = 9.91655
c. log cot A = 0.11975
d. log tan A = 0.06323

Answer 1

1. Using exact values, find the numerical value of :
a. sin 30* cos 240* + sin 210* sin 300*
½*-½ + (-½)(-√(3)/2) = -¼ + √(3)/4

b. tan 225* + tan (-45*)
1 + (-1) = 0

2. Express each of the following as the same function of a positive acute angle:
a. cos 112* 33' = -cos 67° 27'
b. tan 310* = -tan 50°
c. cot 138* 15' 10" = -cot 41° 44' 50"
d. sin (-140*) = -sin 40°

3. Express each as a function of 0:
a. sin (270* + 0) = -cos 0°
b. tan 310* = -1.19175cos 0°
c. tan (810* + 0) = 1/tan 0°
d. sin (0-180*) - sin 0°

4. Find the value of:
a. log sin 62* 22' 33" = -.0525623137
b. log cot 28* 13' 17" = .2702878049
c. log cos 125* 15' 23" = undefined (no log for a negative number)
d. log tan 78* 45' 50" = .7018887347

5. Find the acute angle A, to the nearest second when:
a. log cos A = 9.12575 none - cosine never has values greater than 1
b. log sin A = 9.91655 none - sine never has values greater than 1
c. log cot A = 0.11975 = 37° 11' 56"
d. log tan A = 0.06323 = 49° 9' 23"

...

Answer 2

Way too much material for one question.

1. Using exact values, fine the numerical value of :
a. sin 30° cos 240° + sin 210° sin 300°

sin 30° cos 240° + sin 210° sin 300°
= (sin 30°)(-cos 60°) + (sin 30°)(-sin 60°)
= (1/2)(-1/2) + (-1/2)(-√3/2) = -1/4 + √3/4 = (√3 - 1)/4

b. tan 225° + tan (-45°)

tan 225° + tan (-45°)
= tan 45° - tan 45° = 0

Answer 3

Instead of solving this for you, you might find this helpful:

is the cartesian plane familiar?

you find points thru the coordinates remember? something that looks like (x,y).

the x-coordinate is the cos and y is the sin. therefore, it is (cos,sin).

sec = 1/cos
csc = 1/sin
tan = sin/cos
cot = cos/sin

take it from there. by the way, at 0*, you are at (0,1). when you move 90* to the right, you go to (1,0). move another 90 (that means you're already at 180*, you're at (0,-1). take another 90 and you are at 270*. there, your coordinates are (-1,0).

now try to do the computations yourself. good luck.

EDIT: if you go negative, -90* for example, that means you move the other way around, which is to your left. so, if you moved 90* to your left, that means you moved 270* to your right. so take the coordinates of 270*.

Answer 4

1.
a)sin30*cos(90*3-30) + sin(90 *3-60)sin(90*4-60)
sin30*sin30 +(-cos60)(-sin60)
3/4+ root3/2