trig functions?

Question

If tan pheta = 1/10 what does sine pheta equal?

If cos pheta=2/square root of 10 what does tan pheta equal?

Answer 1

Let sin(pheta) = x
we have: 1/10 = tan(pheta) = sin(pheta) /cos(pheta) = x/sqrt(1 - x^2)
or: 10x = sqrt(1 - x^2)
x = sqrt(101)/101 when pheta is in the first quadrant.
x = -sqrt(101)/101 when pheta is in the thirdt quadrant.

cos(pheta)=2/sqrt(10)
sin(pheta) = +- sqrt[1 - cos^2(pheta)]
= +- sqrt[1 - 4/10]
= +- sqrt(15)/5
tan(pheta) = sin(pheta) /cos(pheta) = sqrt(6)/2 when pheta is in the first quadrant.
tan(pheta) = sin(pheta) /cos(pheta) = -sqrt(6)/2 when pheta is in the fourth quadrant.

Answer 2

1. tan pheta = .1
tan inverse .1 = 5.710...
cos 5.7 = 0.995

2. cos pheta = 2/(square root of 10) = 2/3.16 = .6329
inverse of cos .6329 = 50.734
tan 50.734 = 1.223

Answer 3

No, you ought to cope with the squared as break away the sin. so which you have (f(x))^2, the place f(x) = sin(x/6). applying the chain rule then, you first take the spinoff of the ^2 area. that provides you: 2*sin(x/6) Now, by ability of the chain rule, you ought to multiply that by ability of the spinoff of the interior area, that's sin(x/6). so as that provides you cos(x/6). so far, you presently have: 2*sin(x/6)*cos(x/6) Now, lower back by ability of the chain rule, you ought to take the spinoff of what's interior the cos, it somewhat is x/6. you do no longer choose the quotient rule right here. purely cope with it as (a million/6)*x. The spinoff of which would be in effortless terms a million/6. So interior the tip, you have: 2*sin(x/6)*cos(x/6)*(a million/6) = (a million/3)*sin(x/6)*cos(x/6)