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bekas [8.4K]
3 years ago
8

When do we use the addition and subtraction formulas for sine or cosine?

Mathematics
1 answer:
777dan777 [17]3 years ago
4 0
When we need the cosine of the sum of two angles, we use the addition formula for cosine.

When we need the sine of the difference of two angles, we use the difference formula for sine.

Let's try one.  Say we needed to know

 \cos 15^\circ


We're only expected to know the trig functions of 30/60/90 and 45/45/90 triangles.  Fortunately, 15^\circ = 45^\circ - 30^\circ so

\cos 15^\circ = \cos( 45^\circ - 30^\circ )

= \cos( 45^\circ) \cos(30^\circ ) + \sin(45^\circ) \sin(30^\circ)

= \dfrac{\sqrt{2}}{2} \cdot \dfrac{ \sqrt{3}}{2} + \dfrac{\sqrt{2}}{2} \cdot \dfrac{1}{2}

\cos 15^\circ = \frac{1}{4} (\sqrt{6} + \sqrt{2})



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Tell whether the lines through the given points are parallel, perpendicular, or neither.
antoniya [11.8K]

Answer:

The Slope of Line 1 is ->  -\frac{2}{9}

The Slope of Line 2 is -> -\frac{9}{2}

These two lines are - >  Perpendicular

Step-by-step explanation:

To find the slope of line one, you follow these steps:

First Coordinate 10 -> x1, 5 -> y1

Second Coordinate -8 -> x2, 9 -> y2

Then insert the assigned values into this equation:  \frac{y2-y1}{x2-x1} -> \frac{9-5}{-8-10} which equals \frac{4}{-18} which simplifies to -\frac{2}{9}

Then do the same process to find the slop of line 2:

First Coord: 2 -> x1, -4 -> y1

Second Coord: 11 -> x2, -6 -> y2

Then insert the values into this equation: \frac{y2-y1}{x2-x1}  ->\frac{11-2}{-6-(-4)} which equals \frac{9}{-2}.

We know the lines are perpendicular by:

a. Typing the equations of the lines into a graphing calculator and observing the graph

b. Looking at the slopes. By looking at the slopes, we see that the slope of line 1 is the reciprocal of line 2, and vice versa. Since reciprocal slopes indicate perpendicular lines, the lines 1 and 2 are perpendicular to each other.

Hope this helps!

5 0
3 years ago
Help please :c!
LUCKY_DIMON [66]

Answer:

see the procedure

Step-by-step explanation:

we know that

m∠1+m∠2=180° -----> supplementary angles (form a linear pair)

we have

m∠1=27° ----> given problem

substitute the measure of m∠1 in the equation above and solve for m∠2

27°+m∠2=180°

Subtract 27° both sides

27°+m∠2-27°=180°-27° ----> by subtraction property of equality

m∠2=153°

4 0
3 years ago
Which function BEST expresses the linear relationship displayed by the scatter plot?
Harrizon [31]

Answer:

C

Step-by-step explanation:

We want a line of best fit, which means we want to create a line that the data points will lie closest to.

One thing we can do is find the slope between the bottom-leftmost point and the top-rightmost point. This is because if we were to draw a line connecting these two, it will cut through the data quite well.

Those two points are (9, 15) and (16, 18), so the slope is change in y divided by the change in x:

(18 - 15) ÷ (16 - 9) = 3 ÷ 7 ≈ 0.4

Eliminate A and B.

Now we need to determine the y-intercept. This needs no calculations; simply look at the graph: there's no way a line cutting through the y-intercept point of (0, 18) will perfectly match the data points; instead it must be a y-intercept lower than 18. So, eliminate D.

The answer is C.

6 0
3 years ago
Read 2 more answers
What's 9×9(0+1)=??? And please show work
leva [86]
9 x 9( 0+1)=
81(0+1)=
The answer is 81
Hope this helps!
can I pls get a brainleist?
6 0
3 years ago
Read 2 more answers
A wire with a length of 100 cm is cut into three parts. The length of wire of the first and second parts are the same. The lengt
dsp73

The first two pieces are the same, let each of those equal x, so you have x + x = 2x

The 3rd piece is the sum of the first two + 4, so this would be 2x + 4

Now you have 2x + 2x + 4 = 100 cm

Combine like terms:

4x +4 = 100

Subtract 4 from both sides

4x = 96

Divide both sides by 4

X = 24

First piece is 24 cm

Second piece is 24 cm

Third piece is 52 cm

8 0
2 years ago
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