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Lesson Example Discussion Quiz: Class Homework

Step-2

Title: Trigonometry function( sine, cosine, tangent)

Grade: 1400-a Lesson: S3-L1

Explanation: Hello Students, time to practice and review the steps for the problem.

Lesson Steps

Step	Type	Explanation	Answer
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:	Now plug the value in the formula and make it simpler	\$cos^2(θ) = 1 − sin^2(θ)\$
5	Step	\$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	Formula:	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	Step	Therefore, in Quadrant II, if \$sin⁡θ=3/5\$, then \$cos⁡θ =−4/5\$ and \$tan⁡θ = −3/4\$.
11	Sumup	Can you summarize what you’ve understood in the above steps?
12	Choice.A	This is not correct because it provides incorrect values for cos⁡(θ) and tan⁡(θ)	\$ - 4/5\$, \$ - 3/7\$
13	Choice.B	This is not correct because it provides incorrect values for cos⁡(θ) and tan⁡(θ)	\$ 5/4\$, \$ - 4/3\$
14	Choice.C	This is correct. It has accurately done the calculations based on the formula	\$ - 4/5\$, \$ - 3/4\$
15	Choice.D	This is not correct because it provides incorrect values for cos⁡(θ) and tan⁡(θ)	\$ - 4/3\$, \$ 3/7\$
16	Answer	Option	C
17	Sumup	Can you summarize what you’ve understood in the above steps?

Step

Type

Explanation

Answer

Problem

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

Step

The given values are

sin \$ \theta = 3/5\$ and \$ \theta\$

cos(\$ \theta\$ ) and tan(\$ \theta\$ )

Hint

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

Formula:

Now plug the value in the formula and make it simpler

\$cos^2(θ) = 1 − sin^2(θ)\$

Step

\$cos^2(θ) = 1 − (3/5)^2\$

\$cos^2(θ) = 1 - (9)/25\$

\$cos^2(θ) = -16 /25\$

Step

After simplification

\$cosθ = - 4/5\$ in Quadrant II

Formula:

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

\$tanθ = sinθ / cosθ\$

Step

Now plug the value in the formula

\$tanθ = (3/5) / (-4/5)\$

Step

After simplification

\$tanθ = -3/4\$

Step

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

Sumup

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

Choice.A

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

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

Choice.B

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

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

Choice.C

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

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

Choice.D

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

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

Answer

Option

Sumup

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