Question
Assuming that $\sin u=\frac{3}{5}$ and $\sin v=\frac{4}{5}$ and that $u$ and $v$ are between 0 and $\pi / 2$, evaluate each of the following exactly.$$\sin (u-v)$$
Step 1
We can use the Pythagorean identity $\sin^2 u + \cos^2 u = 1$ to find $\cos u$. So, $\cos^2 u = 1 - \sin^2 u = 1 - \left(\frac{3}{5}\right)^2 = 1 - \frac{9}{25} = \frac{16}{25}$. Taking the square root of both sides, we get $\cos u = \frac{4}{5}$. Show more…
Show all steps
Your feedback will help us improve your experience
Vysakh M and 73 other Precalculus educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Assuming that $\sin u=\frac{3}{5}$ and $\sin v=\frac{4}{5}$ and that $u$ and vare between 0 and $\pi / 2,$ evaluate each of the following exactly. $$\sin (u-v)$$
Trigonometric Identities, Inverse Functions, and Equations
Identities: Pythagorean and Sum and Difference
Assuming that $\sin u=\frac{3}{5}$ and $\sin v=\frac{4}{5}$ and that $u$ and $v$ are between 0 and $\pi / 2,$ evaluate each of the following exactly. $$\cos (u-v)$$
Assuming that $\sin u=\frac{3}{5}$ and $\sin v=\frac{4}{5}$ and that $u$ and $v$ are between 0 and $\pi / 2,$ evaluate each of the following exactly. $$\cos (u+v)$$
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD