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Rudik [331]
3 years ago
6

Trigonometric identities assignment 4

Mathematics
1 answer:
kykrilka [37]3 years ago
6 0

Answer:

<em>Answer: choice D.</em>

Step-by-step explanation:

<u>Trigonometric Functions</u>

We need to recall some properties and definitions of the trigonometric functions.

\displaystyle \tan \theta=\frac{\sin\theta}{\cos\theta}

\displaystyle \sec \theta=\frac{1}{\cos\theta}

We need to simplify the following expression:

5\sin\theta\sec\theta

Substituting the identity for the secant:

\displaystyle 5\sin\theta\sec\theta=5\sin\theta.\frac{1}{\cos\theta}

Operating:

\displaystyle 5\sin\theta\sec\theta=5\frac{\sin\theta}{\cos\theta}

Substituting the definition of the tangent:

\displaystyle 5\sin\theta\sec\theta=5\tan\theta

Correct choice D.

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Answer:

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Step-by-step explanation:

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4 0
3 years ago
Explain how to write a quadratic equation given the following three points on the graph (5,31) (3,11) (0,11)
masha68 [24]

Given:

The graph of a quadratic function passes through the points (5,31) (3,11) (0,11).

To find:

The equation of the quadratic function.

Solution:

A quadratic function is defined as:

y=ax^2+bx+c            ...(i)

It is passes through the point (0,11). So, substitute x=0,y=11 in (i).

11=a(0)^2+b(0)+c

11=c

Putting c=11 in (i), we get

y=ax^2+bx+11               ...(ii)

The quadratic function passes through the point (5,31). So, substitute x=5,y=31 in (ii).

31=a(5)^2+b(5)+11

31-11=a(25)+5b

20=25a+5b

Divide both sides by 5.

4=5a+b                  ...(iii)

The quadratic function passes through the point (3,11). So, substitute x=3,y=11 in (ii).

11=a(3)^2+b(3)+11

11-11=a(9)+3b

0=9a+3b

Divide both sides by 3.

0=3a+b                 ...(iv)

Subtracting (iv) from (iii), we get

4-0=5a+b-3a-b

4=2a

\dfrac{4}{2}=a

2=a

Putting a=2 in (iv), we get

0=3(2)+b

0=6+b

-6=b

Putting a=2,b=-6 in (ii), we get

y=(2)x^2+(-6)x+11

y=2x^2-6x+11

Therefore, the required quadratic equation is y=2x^2-6x+11.

7 0
3 years ago
What is the equation of the line that passes through the point (−8,3) and has a slope of -1/4?
tensa zangetsu [6.8K]

Answer:

y=-1/4x+1

Step-by-step explanation:

so here are my steps after plugging in the numbers:

y-3=-1/4(x+8)

y-3=-1/4x-2

y=-1/4x+1

6 0
3 years ago
Please help me with 13 and 15 asap
Law Incorporation [45]
Gosh, I've done this problem before. Let's start with 13. In this problem, we're basically just skip counting. For example, in the roses row, in the second bouquet, we know we have to add 4 more flowers, so we can document 8. Continue to skip count for both. For 15, we would have about 96 more movie posters remaining, making our ratio 96:x. So, 96:x = 120:100. Therefore, x would equal 80- as 96:80 equals 120:100. If she needs 80 and already had 100, she should sell 20 posters. Hope this helped.
3 0
3 years ago
Find the length x (I'm giving 10 points if you answer this question wrong just to get the 10 points I will report your account)
Natali5045456 [20]
Okay so here's how i think you solve it


both triangles have the same ratio, so set it as 3/4.5 (the smaller triangle) is equal to X/13.5 (the 9 added to the 4.5)

multiply 13.5/1 on both sides to get x alone

13.5 3
-------- x ------- = x x= 9
1 4.5
5 0
3 years ago
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