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Lesson Example Discussion Quiz: Class Homework

Step-5

Title: Trigonometry function( sine, cosine, tangent)

Grade: 10-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	Evaluate the following expression: \$ sin(pi/3) cos(pi/6) + cos(pi/3) sin(pi/6) \$.
2	Step	Let’s evaluate the given expression step by step:	\$ sin(pi/3) cos(pi/6) + cos(pi/3) sin(pi/6) \$
3	Hint	First, let’s use the trigonometric identities:	\$ sin(pi/3) = \sqrt3 / 2 \$ \$ cos(pi/3) = 1/2 \$ \$ sin(pi/6) = 1/2 \$ \$ cos(pi/6) = \sqrt3 / 2 \$
4	Step	Now substitute these values into the expression:	\$ \sqrt3 / 2 * \sqrt3 / 2 + 1/2 * 1/2 \$
5	Step	Simplify further:	\$ 3/4 + 1/4 \$
6	Step	Combine the terms:	\$ 4/4 = 1 \$
7	Step	So, the evaluated value of the expression is 1.
8	Choice.A	This is correct because the result equals 1 after evaluation	1
9	Choice.B	This is incorrect because after the evaluation the result is not 1	\$ 1/2\$
10	Choice.C	The evaluation yields a result other than 1, making this statement incorrect	\$ \sqrt3/2\$
11	Choice.D	The evaluation yields a result other than 1, thus rendering this statement incorrect	\$ \sqrt 3\$
12	Answer	Option	A
13	Sumup	Can you briefly tell me what you’ve learned and understood in today’s lesson?

Step

Type

Explanation

Answer

Problem

Evaluate the following expression: \$ sin(pi/3) cos(pi/6) + cos(pi/3) sin(pi/6) \$.

Step

Let’s evaluate the given expression step by step:

\$ sin(pi/3) cos(pi/6) + cos(pi/3) sin(pi/6) \$

Hint

First, let’s use the trigonometric identities:

\$ sin(pi/3) = \sqrt3 / 2 \$

\$ cos(pi/3) = 1/2 \$

\$ sin(pi/6) = 1/2 \$

\$ cos(pi/6) = \sqrt3 / 2 \$

Step

Now substitute these values into the expression:

\$ \sqrt3 / 2 * \sqrt3 / 2 + 1/2 * 1/2 \$

Step

Simplify further:

\$ 3/4 + 1/4 \$

Step

Combine the terms:

\$ 4/4 = 1 \$

Step

So, the evaluated value of the expression is 1.

Choice.A

This is correct because the result equals 1 after evaluation

Choice.B

This is incorrect because after the evaluation the result is not 1

\$ 1/2\$

Choice.C

The evaluation yields a result other than 1, making this statement incorrect

\$ \sqrt3/2\$

Choice.D

The evaluation yields a result other than 1, thus rendering this statement incorrect

\$ \sqrt 3\$

Answer

Option

Sumup

Can you briefly tell me what you’ve learned and understood in today’s lesson?