SOLUTION: 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. Yo
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Question 691184: 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 (theta) = 3/x
(b) x = 4 cos (theta)
(c) tan (theta) = x
Found 2 solutions by stanbon, lwsshak3:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
answered
Answer by lwsshak3(11628) (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 (theta) = 3/x
(b) x = 4 cos (theta)
(c) tan (theta) = x
**
Use the following notation: O=opposite side, A=adjacent side, H=hypotenuse
..
(a) sin (theta) = 3/x=O/H
O=3
H=x
A=√(H^2-O^2)=√(x^2-3^2)=√(x^2-9)
cos (theta)=A/H=√(x^2-9)/x
tan (theta)=O/A=3/√(x^2-9)
..
b) x = 4 cos (theta)
cos (theta)=x/4=A/H
A=x
H=4
O=√(H^2-A^2)=√(4^2-x^2)=√(16-x^2)
sin(theta)=O/H=√(16-x^2)/4
tan (theta)=O/A=√(16-x^2)/x
(c) tan (theta) = x=O/A
O=x
A=1
H=√(O^2+A^2)=√(x^2+1^2)=√(x^2+1)
cos (theta)=A/H=1/√(x^2+1)
sin(theta)=O/H=x/√(x^2+1)
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