From the trigonometry:
tan θ = (sin θ) / (cos θ)
cot θ = (cos θ) / (sin θ)
∴ tan θ + cot θ = (sin θ) / (cos θ) + (cos θ) / (sin θ)
= [ sin² θ + cos² θ]/( sin θ cos θ) = 1 /( sin θ cos θ )
note : sin² θ + cos² θ = 1
Solution,
y = -x-4......(i)
3x + y =- 16.......(ii)
Now,
Substituting the value of y in equation (ii)
or, 3x + (-x-4)= -16
or,3x - x - 4 = -16
or, 2x= -16 +4
or, x = -12/2
: x = -6
Then,
Substituting the value of x in (i) equation;
or,y= -(-6) - 4
or,y= 6 - 4
: y =2
Answer:
8.0
Step-by-step explanation:
Sin theta = opposite /hypotenuse
sin 53 = x/10
Multiply each side by 10
10 sin 53 = x
7.9863551
To the nearest tenth
x = 8.0
Eq1) 2r+2s=50
eq2) 2r-s=17
solve for s in equation2 (eq2)
-s=17-2r
s=-17+2r
Substitute s into equation1 (eq1)
2r+2(-17+2r)=50
2r-34+4r=50
6r-34=50
6r=50+34
6r=84
r=14
Substitute into either equation and solve for s
2(14)-s=17
28-s=17
-s=17-28
-s=-11
s=11
The slope of the line is 2/3
