If x = 5 sin θ, use trigonometric substitution to write as a trigonometric function of θ, where .
A)5 sin θ
B)5 cos θ
C)5 tan θ
D)5 csc θ
E)5 sec θ

Question

If x = 5 sin θ, use trigonometric substitution to write  as a trigonometric function of θ, where  .
A)​5 sin θ 
B)​5 cos θ 
C)​5 tan θ 
D)​5 csc θ 
E)​5 sec θ

Quizplus · Accepted Answer

We can use the Pythagorean identity to get
$$\sqrt{11^2-5^2\sin^2	heta}=\sqrt{11^2-25\cos^2	heta}$$
Now, let $x=5\sin	heta$ so that $\sin	heta=\frac{x}{5}$ and $\cos	heta=\sqrt{1-\sin^2	heta}=\sqrt{1-\frac{x^2}{25}}$. Substituting, we have
$$\sqrt{11^2-25\cos^2	heta}=\sqrt{11^2-25\left(1-\frac{x^2}{25}ight)}=\sqrt{x^2+86}$$
Therefore, the expression becomes $\boxed{5\cos	heta=5\sqrt{1-\sin^2	heta}=5\sqrt{1-\frac{x^2}{25}}=\sqrt{25-x^2}}.$

If X = 5 Sin θ, Use Trigonometric Substitution to Write