Question 691180: The following problems give an expression for one of the three functions sin , cos, or tan ,with (theta) in the fi rst quadrant. Find expressions for the other two functions. Your answers will be algebraic expressions of x.
(a) sin = 3=x
(b) x = 4 cos
(c) tan = x
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! The following problems give an expression for one of the three functions sin , cos, or tan ,with (theta) in the fi rst quadrant. Find expressions for the other two functions. Your answers will be algebraic expressions of x.
(a) sin = 3/x
Since sin = opp/hyp, opp = 3 and hyp = x
Then adj = sqrt[x^2-3^2] = sqrt[x^2-9]
cos = sqrt(x^2-9)/x
tan = (3/x)/[(x^2-9)]/x] = 3/(x^2-9)
---------------------------------------
(b) x = 4 cos
cos = x/4
Since cos = adj/hyp, adj = x and hyp = 4
Then opp = sqrt[4^2-x^2]
---
sin = opp/hyp = sqrt(16-x^2)/4
tan = opp/adj = sqrt(16-x^2)/x
======================================
(c) tan = x/1
Since tan = opp/adj, opp = x and adj = 1
---
Then hyp = sqrt(x^2+1]
sin = x/sqrt(x^2+1)
cos = 1/sqrt(x^2+1)
===========================
Cheers,
Stan H.
|
|
|
