Question

question 6 of 20
there are values of t so that \\(\sin t = .6\\) and \\(\cos t = .8\\)
\\(\bigcirc\\) a. true
\\(\bigcirc\\) b. false

Explanation:

Step1: Recall Pythagorean identity

The Pythagorean identity for sine and cosine is $\sin^2 t + \cos^2 t = 1$.

Step2: Substitute given values

Substitute $\sin t = 0.6$ and $\cos t = 0.8$ into the identity: $(0.6)^2 + (0.8)^2$.
Calculate each square: $0.6^2 = 0.36$ and $0.8^2 = 0.64$.

Step3: Sum the squares

Add the two results: $0.36 + 0.64 = 1$.
This satisfies the Pythagorean identity, so there exist values of $t$ (e.g., in the first quadrant) where $\sin t = 0.6$ and $\cos t = 0.8$.

Answer:

A. True