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3 years ago

How to find the exact value of each trigonometric function without a calculator?

Mathematics

1 answer:

Goryan [66]3 years ago

5 0

Remember them is the best way to go.
draw the exact value triangles if you're unsure, but importantly, you just need to memorise these exact values.

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Find the sum of the first 8 terms of the series. 1/2 + 1 + 2 + 4

Roman55 [17]

$\bf \cfrac{1}{2}~~,~~\stackrel{2\cdot \frac{1}{2}}{1}~~,~~\stackrel{2\cdot 1}{2}~~,~~\stackrel{2\cdot 2}{4}~~,...$

so as you can see the common ratio is 2, and the first term is 1/2,

$\bf \qquad \qquad \textit{sum of a finite geometric sequence} \\\\ S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=n^{th}\ term\\ a_1=\textit{first term's value}\\ r=\textit{common ratio}\\ ----------\\ r=2\\ a_1=\frac{1}{2}\\ n=8 \end{cases} \\\\\\ S_8=\cfrac{1}{2}\left( \cfrac{1-2^8}{1-2} \right)\implies S_8=\cfrac{1}{2}\left( \cfrac{-255}{-1} \right)\implies S_8=\cfrac{255}{2}$

4 0

4 years ago

Read 2 more answers

Write an equation of the line that passes through the given point and is (a) parallel and (b) perpendicular to the given line.

inessss [21]

Answer:

(a). y = 3x - 11 ; (b). y = $-\frac{1}{3}$ x - 1

Step-by-step explanation:

Parallel lines have the same slopes

Slopes of perpendicular lines are opposite reciprocals.

(3, - 2)

The slope of given line is 3

(a). Equation of ║ line is

y + 2 = 3(x - 3)

y = 3x - 11

(b). Slope of perpendicular line is $-\frac{1}{3}$

y + 2 = $-\frac{1}{3}$ (x - 3)

y =  $-\frac{1}{3}$  x - 1

5 0

3 years ago

Read 2 more answers

Which of the following is one of the factors of the polynomial

RUDIKE [14]

Answer:

5x-2

Step-by-step explanation:

15x^2-x-2

15x^2+5x-6x-2

factorize

5x(3x+1)-2(3x+1)

Sol: (3x+1)*(5x-2)

7 0

3 years ago

A coffee packaging plant claims that the mean weight of coffee in its containers is at least 32 ounces. A random sample of 15 co

Luda [366]

Answer:

We conclude that the mean weight of coffee in its containers is at least 32 ounces which means that the data support the claim.

Step-by-step explanation:

We are given that a coffee packaging plant claims that the mean weight of coffee in its containers is at least 32 ounces.

A random sample of 15 containers were weighed and the mean weight was 31.8 ounces with a sample standard deviation of 0.48 ounces.

Let $\mu$ = mean weight of coffee in its containers.

SO, Null Hypothesis, $H_0$ : $\mu \geq$ 32 ounces {means that the mean weight of coffee in its containers is at least 32 ounces}

Alternate Hypothesis, $H_A$ : $\mu$ < 32 ounces {means that the mean weight of coffee in its containers is less than 32 ounces}

The test statistics that would be used here One-sample t-test statistics as we don't know about population standard deviation;

T.S. = $\frac{\bar X-\mu}{\frac{s}{\sqrt{n} } }$ ~ $t_n_-_1$

where, $\bar X$ = sample mean weight = 31.8 ounces

s = sample standard deviation = 0.48 ounces

n = sample of containers = 15

So, the test statistics = $\frac{31.8 -32}{\frac{0.48}{\sqrt{15} } }$ ~ $t_1_4$

= -1.614

The value of t test statistics is -1.614.

Now, at 0.01 significance level the t table gives critical value of -2.624 at 14 degree of freedom for left-tailed test.

Since our test statistic is more than the critical value of t as -1.614 > -2.624, so we have insufficient evidence to reject our null hypothesis as it will not fall in the rejection region due to which we fail to reject our null hypothesis.

Therefore, we conclude that the mean weight of coffee in its containers is at least 32 ounces which means that the data support the claim.

8 0

4 years ago

Samantha spent 40 minutes on homework. Sixty percent of that time was spent on language arts.how many minutes were spent on lang

yan [13]

If you would like to know how many minutes were spent on language arts, you can calculate this using the following steps:

60% of 40 minutes = 60% * 40 = 60/100 * 40 = 24 minutes

The correct result would be: 24 minutes were spent on language arts.

3 0

4 years ago

Read 2 more answers