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2 years ago

Write the expression as the sine or cosine of an angle pi/5 cos pi/2+sin pi/2\cos pi/5

Mathematics

1 answer:

vova2212 [387]2 years ago

7 0

The given expression as a sine function is $sin(\frac{\pi}{5} +\frac{\pi}{2} )$

<h3>The addition formula for trigonometry</h3>

The given expression is:

$sin(\frac{\pi}{5})cos(\frac{\pi}{2} ) + cos(\frac{\pi}{5})sin(\frac{\pi}{2} )$

Note that:

$sin(A+B)=sinAcosB+cosAsinB$

Applying the addition principle to the given expression, we have:

$sin(\frac{\pi}{5})cos(\frac{\pi}{2} ) + cos(\frac{\pi}{5})sin(\frac{\pi}{2} )=sin(\frac{\pi}{5} +\frac{\pi}{2} )$

Therefore, the given expression as a sine function is $sin(\frac{\pi}{5} +\frac{\pi}{2} )$

Learn more on addition formula of trigonometry here: brainly.com/question/22852405

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-4(2p + 5) + 8p = -11

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Answer:

There are no values of P to make it true

Step-by-step explanation:

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3 years ago

Choose the correct simplification of f^9 h^23/f^3 h^17

Tanzania [10]

Answer:

f6h40

Step-by-step explanation:

Step 1 :

h23

Simplify ———

Equation at the end of step 1 :

h23

((f9) • ———) • h17

Step 2 :

Multiplying exponential expressions :

2.1 h23 multiplied by h17 = h(23 + 17) = h40

Final result :

f6h40

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3 years ago

The hourly wage increase each employee receives each year depends on their number of years of service. Every three years of serv

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Answer:

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3 years ago

Maths functions question!!

Marina86 [1]

Answer:

5) DE = 7 units and DF = 4 units

6) ST = 8 units

$\textsf{7)} \quad \sf OM=\dfrac{3}{2}\:units$

8) x ≤ -3 and x ≥ 3

Step-by-step explanation:

<u>Information from Parts 1-4:</u>

brainly.com/question/28193969

$f(x)=-x+3$

$g(x)=x^2-9$

A = (3, 0) and C = (-3, 0)

Points A and D are the <u>points of intersection</u> of the two functions.

To find the x-values of the points of intersection, equate the two functions and solve for x:

$\implies g(x)=f(x)$

$\implies x^2-9=-x+3$

$\implies x^2+x-12=0$

$\implies x^2+4x-3x-12=0$

$\implies x(x+4)-3(x+4)=0$

$\implies (x-3)(x+4)=0$

Apply the zero-product property:

$\implies (x-3)= \implies x=3$

$\implies (x+4)=0 \implies x=-4$

From inspection of the graph, we can see that the x-value of point D is <u>negative</u>, therefore the x-value of point D is x = -4.

To find the y-value of point D, substitute the found value of x into one of the functions:

$\implies f(-4)=-(-4)=7$

Therefore, D = (-4, 7).

The length of DE is the difference between the y-value of D and the x-axis:

⇒ DE = 7 units

The length of DF is the difference between the x-value of D and the x-axis:

⇒ DF = 4 units

To find point S, substitute the x-value of point T into function g(x):

$\implies g(4)=(4)^2-9=7$

Therefore, S = (4, 7).

The length ST is the difference between the y-values of points S and T:

$\implies ST=y_S-y_T=7-(-1)=8$

Therefore, ST = 8 units.

The given length of QR (⁴⁵/₄) is the difference between the functions at the same value of x. To find the x-value of points Q and R (and therefore the x-value of point M), subtract g(x) from f(x) and equate to QR, then solve for x:

$\implies f(x)-g(x)=QR$

$\implies -x+3-(x^2-9)=\dfrac{45}{4}$

$\implies -x+3-x^2+9=\dfrac{45}{4}$

$\implies -x^2-x+\dfrac{3}{4}=0$

$\implies -4\left(-x^2-x+\dfrac{3}{4}\right)=-4(0)$

$\implies 4x^2+4x-3=0$

$\implies 4x^2+6x-2x-3=0$

$\implies 2x(2x+3)-1(2x+3)=0$

$\implies (2x-1)(2x+3)=0$

Apply the zero-product property:

$\implies (2x-1)=0 \implies x=\dfrac{1}{2}$

$\implies (2x+3)=0 \implies x=-\dfrac{3}{2}$

As the x-value of points M, Q and P is negative, x = -³/₂.

Length OM is the difference between the x-values of points M and the origin O:

$\implies x_O-x_m=o-(-\frac{3}{2})=\dfrac{3}{2}$

Therefore, OM = ³/₂ units.

The values of x for which g(x) ≥ 0 are the values of x when the parabola is above the x-axis.

Therefore, g(x) ≥ 0 when x ≤ -3 and x ≥ 3.

8 0

1 year ago

Read 2 more answers

Arc length for xy I’ve been stuck on this for a while

Contact [7]

Answer:

12.22

Step-by-step explanation:

There are 360° in a full circle

The circumference of a circle is c = 2πr

----------------------------------

The lenght of the arc will be the portion of the circumferece included in the angle

l = (∅/360) * 2πr

plug in the knowns

l = (70/360) * 2π(10)

l ≈ 12.22

7 0

3 years ago