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Sveta_85 [38]
3 years ago
15

Assume that theta is a positive acute angle.

Mathematics
1 answer:
muminat3 years ago
6 0

Answer:

Step-by-step explanation:sin

(

θ

)

=

40

41

Use the definition of sine to find the known sides of the unit circle right triangle. The quadrant determines the sign on each of the values.

sin

(

θ

)

=

opposite

hypotenuse

Find the adjacent side of the unit circle triangle. Since the hypotenuse and opposite sides are known, use the Pythagorean theorem to find the remaining side.

Adjacent

=

√

hypotenuse

2

−

opposite

2

Replace the known values in the equation.

Adjacent

=

√

(

41

)

2

−

(

40

)

2

Simplify

√

(

41

)

2

−

(

40

)

2

.

Tap for more steps...

Adjacent

=

9

Find the value of cosine.

Tap for more steps...

cos

(

θ

)

=

9

41

Find the value of tangent.

Tap for more steps...

tan

(

θ

)

=

40

9

Find the value of cotangent.

Tap for more steps...

cot

(

θ

)

=

9

40

Find the value of secant.

Tap for more steps...

sec

(

θ

)

=

41

9

Find the value of cosecant.

Tap for more steps...

csc

(

θ

)

=

41

40

This is the solution to each trig value.

sin

(

θ

)

=

40

41

cos

(

θ

)

=

9

41

tan

(

θ

)

=

40

9

cot

(

θ

)

=

9

40

sec

(

θ

)

=

41

9

csc

(

θ

)

=

41

40

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Answer:

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Step-by-step explanation:

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To find:

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5 0
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Given three points A(-7, 1), B(m, 6) and P(-1, n). If the point P divides AB internally in the ratio of 3: 2, find the values of
vesna_86 [32]

Answer:

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Step-by-step explanation:

<u>Using Section Formula.</u>

<u />If \ the \ line \ segment \ AB \ where  \ A = (x _1, y_1) \ and \ B = (x_2, y_2) \ divided \ by \ P =(x , y) \ in \ the \ ratio \ a : b,\\\\Then \  the \ points \  of \  P  \ \\\\x = \frac{ax_2 + bx_1}{a+b} \ and \ y = \frac{ay_2 + by_1}{a+b}<u />

   Here (x_1 , y_ 1 ) = ( -7 , 1 ) \ and \ (x_ 2 , y _ 2 ) = (m , 6)\\\\ratio\ a:b  = 3 : 2\\\\Therefore, P (x, y) \\\\x = \frac{3m + (2\times -7)}{5} \ \ \ \ \ \ \ \ \ \ \ [ \ x =  -1 \ ] \\\\-1 = \frac{3m - 14}{5}\\\\- 5 = 3m - 14\\\\-5 + 14 = 3m\\\\9 = 3m \\\\m = 3<u />

  y =\frac{3\times 6 + 2 \times 1}{5}\\\\n = \frac{18 + 2}{5} = \frac{20}{5} = 4

<u />

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