If x = 6 sin θ,use trigonometric substitution to write $\sqrt { 36 - x ^ { 2 } }$ as a trigonometric function of θ,where $0

Question

If x = 6 sin θ,use trigonometric substitution to write $\sqrt { 36 - x ^ { 2 } }$ as a trigonometric function of θ,where $0 < \theta < \frac { \pi } { 2 }$ .
A)​6 csc θ
B)​6 sec θ
C)​6 sin θ
D)​6 cos θ
E)​6 tan θ

Quizplus · Accepted Answer

We can use the identity: 1 - sin^2θ = cos^2θ
1 - (x/6)^2 = cos^2θ
cosθ = ±√(1 - x^2/36)

Since the value of cosθ is positive in the first quadrant and x is positive, we take the positive square root. Therefore, we have:

11ea99db_b4aa_79ba_94ac_9fb623721401_TB4590_11 = 6 cos θ

If X = 6 Sin θ,Use Trigonometric Substitution to Write 36−x2\sqrt { 36 - x ^ { 2 } }36−x2​

If X = 6 Sin θ,Use Trigonometric Substitution to Write $\sqrt { 36 - x ^ { 2 } }$