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2 years ago

If tan 0=3/4 find sin0

Mathematics

1 answer:

bija089 [108]2 years ago

6 0

Answer:

sin O = $\frac{3}{5}$

Step-by-step explanation:

given tan O = $\frac{3}{4}$ = $\frac{opposite}{adjacent}$

Then this is a right triangle with legs 3 and 4

Using Pythagoras' identity then the hypotenuse (h ) is

h = $\sqrt{3^2+4^2}$ = $\sqrt{25}$ = 5, hence

sin O = $\frac{opposite}{hypotenuse}$ = $\frac{3}{5}$

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Anna enjoys dinner at a restaurant in Washington DC where the sales tax on meals is 5%. She leave a 20% tip on the price of her

Maru [420]

Answer:

52.40

Step-by-step explanation:

Discussion

Suppose the meal starts out as x.

She pays 5% of x as a sales tax

So that brings the total up to 100% + 5% = 105%

Before paying, she pays 20% on x as her tip. The tax does not touch the tip.

So that brings the total up to 100% + 5% + 20% = 125% of this is based on x, the cost of the meal.

So 125% of x = 65.50 change the % to a fraction

125/100 * x = 65.50 Multiply both sides by 100/125

125/100 * 100/125x = 100/125 * 65.50

x = 100/125 * 65.50 Multiply by 100

x = 6550 / 125 Divide by 125

Check

Tax = 5% * 52.40 = 5/100 * 52.40 = 2.62

Tip = 20%*52.40 = 20/100 * 52.40=10.48

Meal = 52.40

Total 65.50 Just as it should

8 0

3 years ago

Use the sum and difference identities to find the exact values of the sine, cosine, and tangent of the angle. . 165 = 135 + 30

Serhud [2]

So lets get to the problem

165°= 135° +30° 

To make it easier I'm going to write the same thing like this 
165°= 90° + 45°+30° 

Sin165° 
= Sin ( 90° + 45°+30° ) 
= Cos( 45°+30° )..... (∵ Sin(90 + θ)=cosθ 
= Cos45°Cos30° - Sin45°Sin30° 

Cos165° 
= Cos ( 90° + 45°+30° ) 
= -Sin( 45°+30° )..... (∵Cos(90 + θ)=-Sinθ 
= Sin45°Cos30° + Cos45°Sin30° 

Tan165° 
= Tan ( 90° + 45°+30° ) 
= -Cot( 45°+30° )..... (∵Cot(90 + θ)=-Tanθ 
= -1/tan(45°+30°) 
= -[1-tan45°.Tan30°]/[tan45°+Tan30°] 

Substitute the above values with the following... These should be memorized 
Sin 30° = 1/2 
Cos 30° =[Sqrt(3)]/2 
Tan 30° = 1/[Sqrt(3)] 
Sin45°=Cos45°=1/[Sqrt(2)] 
Tan 45° = 1

4 0

3 years ago

Find the product of the given complex number and its conjugate. 1/5+4i

nasty-shy [4]

Answer:

-15.96

Step-by-step explanation:

A conjugate is a binomial with the sign inside changed. So the conjugate of (1/5 + 4i) is (1/5 - 4i)

Set the original and the conjugate next to each other and F.O.I.L. Multiply the first numbers of each binomial, the 1/5 and the 1/5 to get 1/25. This is the "F."

Multiply the outer members, the 1/5 and the 4i to get - 60i. This is the "O."

Multiply the inner numbers ( the + 4i and the 1/5) to get + 60i. This is the "I."

Multiply the positive 4i and the negative 4i to get 16i squared

The positive 60i and the negative 60i cancel each other out.

The i squared changes into - 1. This makes the 16 negative.

Add 1/25 to - 16 to get - 15.96

4 0

3 years ago

Which of the equations below represents a line perpendicular to the yaxis?

lions [1.4K]

Answer:

A. y=-6

Step-by-step explanation:

Using the answer, it would make a horizontal line which would be perpendicular to the y axis.

4 0

2 years ago

Read 2 more answers

The graph below shows the distance d you run, in miles, as a function of time t, in minutes, during a 5-mile run. Your friend sa

notka56 [123]

The correct answer for this question is this one:

"Your friend says that the graph is not continuous because it stops at d = 5, so the graph is discrete." Your friend is wrong. The graph is still continuous because the graph shows continuity. The problem only shows the graph at certain t time. This means that the graph can be extended at any t time.

4 0

3 years ago