If sin \$ \theta = 3/5\$ and \$ \theta\$ are in Quadrant II, find the values of cos(\$ \theta\$ ) and tan(\$ \theta\$ ).

The given values are

sin \$ \theta = 3/5\$ and \$ \theta\$ cos(\$ \theta\$ ) and tan(\$ \theta\$ )

Given that sin \$ \theta = 3/5\$, we can use the Pythagorean identity \$sin^2(θ) + cos^2(θ) =1 \$to find cosθ.

Now plug the value in the formula and make it simpler

\$cos^2(θ) = 1 − sin^2(θ)\$ \$cos^2(θ) = 1 − (3/5)^2\$ \$cos^2(θ) = 1 - (9)/25\$ \$cos^2(θ) = -16 /25\$

After simplification

\$cosθ = - 4/5\$ in Quadrant II

Now, to find tanθ, we can use the relationship is

\$tanθ = sinθ / cosθ\$

Now plug the value in the formula

\$tanθ = (3/5) / (- 4/5)\$

After simplification

\$tanθ = - 3/4\$

Therefore, in Quadrant II, if \$sin⁡θ = 3/5\$, then \$cos⁡θ = - 4/5\$​ and \$tan⁡θ = - 3/4\$.​

Wrong: Because it states the value of tanθ as \$3/7\$​, which is not the correct value based on our calculations. The correct value of tanθ is \$- 3/4​\$

\$ - 4/5\$, \$ - 3/7\$

Option B is incorrect because the value of cos(θ) is positive, contradicting the fact that θ is in Quadrant II where cosine should be negative. Also, the values for cos(θ) and tan(θ) do not match our calculations

\$ 5/4\$, \$ - 4/3\$

This is correct. It has accurately done the calculations based on the formula

\$ - 4/5\$, \$ - 3/4\$

This is not correct because it provides incorrect values for cos⁡(θ) and tan⁡(θ)

\$ - 4/3\$, \$ 3/7\$

Option

C

Can you summarize what you’ve understood in the above steps?