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2 years ago

Find the sine and cosine of a 60° angle find the sine and cosine of a 30° angle

Mathematics

1 answer:

Ymorist [56]2 years ago

7 0

Answer:

Using the 30-60-90 triangle to find sine and cosine

sin(60 degrees) = 2√3 4.

sin(60 degrees) = √3 2.

sin(30 degrees) = 2 4.

sin(30 degrees) = 1 2.

cos(60 degrees) = 2 4.

cos(60 degrees) = 1 2.

cos(30 degrees) = 2√3 4.

cos(30 degrees) = √3 2.

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One urn contains one blue ball (labeled B1) and three red balls (labeled R1, R2, and R3). A second urn contains two red balls (R

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Answer:

(a) See attachment for tree diagram

(b) 24 possible outcomes

Step-by-step explanation:

Given

$Urn\ 1 = \{B_1, R_1, R_2, R_3\}$

$Urn\ 2 = \{R_4, R_5, B_2, B_3\}$

Solving (a): A possibility tree

If urn 1 is selected, the following selection exists:

$B_1 \to [R_1, R_2, R_3]; R_1 \to [B_1, R_2, R_3]; R_2 \to [B_1, R_1, R_3]; R_3 \to [B_1, R_1, R_2]$

If urn 2 is selected, the following selection exists:

$B_2 \to [B_3, R_4, R_5]; B_3 \to [B_2, R_4, R_5]; R_4 \to [B_2, B_3, R_5]; R_5 \to [B_2, B_3, R_4]$

See attachment for possibility tree

Solving (b): The total number of outcome

For urn 1

There are 4 balls in urn 1

$n = \{B_1,R_1,R_2,R_3\}$

Each of the balls has 3 subsets. i.e.

$B_1 \to [R_1, R_2, R_3]; R_1 \to [B_1, R_2, R_3]; R_2 \to [B_1, R_1, R_3]; R_3 \to [B_1, R_1, R_2]$

So, the selection is:

$Urn\ 1 = 4 * 3$

$Urn\ 1 = 12$

For urn 2

There are 4 balls in urn 2

$n = \{B_2,B_3,R_4,R_5\}$

Each of the balls has 3 subsets. i.e.

$B_2 \to [B_3, R_4, R_5]; B_3 \to [B_2, R_4, R_5]; R_4 \to [B_2, B_3, R_5]; R_5 \to [B_2, B_3, R_4]$

So, the selection is:

$Urn\ 2 = 4 * 3$

$Urn\ 2 = 12$

Total number of outcomes is:

$Total = Urn\ 1 + Urn\ 2$

$Total = 12 + 12$

$Total = 24$

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How do you express sin x + cos x in terms of sine only?

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Answer:

$\sin x + \sqrt{1-\sin^2x}$

Step-by-step explanation:

Given: sin x + cos x

To change the given trigonometry expression in term of sine only.

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$\sin^2x+\cos^2x=1$
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Expression: $\sin x+\cos x$

We get rid of cos x from expression and write as sine form.

Expression: $\sin x + \sqrt{1-\sin^2x}$ $\because \cos x=\sqrt{1-\sin^2x}$

Hence, The final expression is only sine function.

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