1

Problem

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

2

Step

The given values are

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

3

Hint

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

4

Formula

Pythagorean identity is rewritten as \$cos^2(θ) = 1 - sin^2(θ)\$.

5

Step

Now plug the value in the formula and make it simpler:

\$cos^2(θ) = 1 − (3/5)^2\$

\$cos^2(θ) = 1 - (9)/(25)\$

\$cos^2(θ) = - (16) /(25)\$

6

Step

After simplification:

\$cosθ = - 4/5\$ in Quadrant II

7

Step

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

\$tanθ = (sinθ) / (cosθ)\$

8

Step

Now plug the value in the formula:

\$tanθ = (3/5) / (- 4/5)\$

9

Step

After simplification:

\$tanθ = - 3/4\$

10

Solution

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

11

Sumup

Please summarize Problem, Clue, Hint, Formula, Steps and Solution

Choices

12

Choice-A

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​\$

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

13

Choice-B

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

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

14

Choice-C

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

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

15

Choice-D

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

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

16

Answer

Option

C

17

Sumup

Please summarize choices