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2 years ago

How do I solve cos x> 1/2 sin x?

Mathematics

1 answer:

Hatshy [7]2 years ago

4 0

Divide both sides by $\dfrac12\cos x$ :

$\dfrac{\cos x}{\frac12\cos x}>\dfrac{\frac12\sin x}{\frac12\cos x}\implies2>\dfrac{\sin x}{\cos x}=\tan x$

If $-\dfrac\pi2$ , then

$\tan x$

and more generally, for any integer $n$ ,

$n\pi-\dfrac\pi2$

You might be interested in

Isabel walks 1.5km every day. How far does she walk in 5 days? Write your answer in meters

aleksandrvk [35]

----------------------------------
Find 5 days :
----------------------------------
1 day = 1.5km
5 days = 1.5 x 5 = 7.5 km

----------------------------------
Convert km to m
----------------------------------
1 km = 1000 m
7.5km = 7.5 x 1000
7.5 km = 7500 m

--------------------------------------------------------------------
Answer: She walked 7500 m
--------------------------------------------------------------------

4 0

2 years ago

Read 2 more answers

Find the distance between the points (2,3) (-3,-6)

Valentin [98]

Answer:

10.3

Step-by-step explanation:

As we move from (-3,-6) to (2,3), x increases by 5 (this is the horizontal distance between (2,3) and (-3,-6) ) and y decreases by 9 (vertical distance).

We apply the Pythagorean Theorem here:

d^2 = x^2 + y^2, or

d^2 = (5)^2 + (-9)^2 = 25 + 81 = 106

Thus, the distance between (2,3) and (-3,-6) is d = sqrt(106), or approx.

10.3.

7 0

3 years ago

In ΔKLM, l = 570 cm, k = 490 cm and ∠K=46°. Find all possible values of ∠L, to the nearest degree.

Katen [24]

Step-by-step explanation:

In ΔKLM, l = 570 cm, k = 490 cm and ∠K=46°. Find all possible values of ∠L, to the nearest degree.

k = 490

l = 570

46°

?°

\frac{\sin A}{a}=\frac{\sin B}{b}

sinA

sinB

From the reference sheet (reciprocal version).

\frac{\sin L}{570}=\frac{\sin 46}{490}

570

sinL

490

sin46

Plug in values.

\sin L=\frac{570\sin 46}{490}\approx 0.836783

sinL=

490

570sin46

≈0.836783

Evaluate.

L=\sin^{-1}(0.836783)\approx 56.8\approx 57^{\circ}

L=sin

−1

(0.836783)≈56.8≈57

∘

Inverse sine and round.

\text{Quadrant II: } 180-57=123^{\circ}

Quadrant II: 180−57=123

∘

Sine is positive in quadrants 1 and 2.

\text{Check for possibility:}

Check for possibility:

No triangle's angles may add to more than 180.

46+57=103

∘

←Possible

Less than 180.

46+123=169}

46+123=169

∘

←Possible

Less than 180.

Answer: 57

and 123

5 0

3 years ago

Plz do both of them for me and even show the work plzzzzzz

Vinvika [58]

Answer:

(a)= option 3

(b)= option 3

Step-by-step explanation:

(A) It is given that a sequence is defined by the recursive function $a_{1}=1$ and $a_{n}=a_{n-1}+n$

Now, substituting the value of n=2 in above equation,

$a_{2}=a_{1}+2$

$a_{2}=1+2$

$a_{2}=3$

Again putting n=3,

$a_{3}=a_{2}+3$

$a_{3}=3+3$

$a_{2}=6$

Putting n=4,

$a_{4}=a_{3}+4$

$a_{4}=6+4$

$a_{4}=10$

Putting n=5,

$a_{5}=a_{4}+5$

$a_{5}=10+5$

$a_{5}=15$

Putting n=6,

$a_{6}=a_{5}+6$

$a_{6}=15+6$

$a_{6}=21$

Putting n=7,

$a_{7}=a_{6}+7$

$a_{7}=21+7$

$a_{7}=28$

Hence, option 3 is correct.

(B) The given sequence is :

5, -10, 20, -40, 80.....

Since, the given sequence is GP, therefore

$a_{1}=5$ and r=-2

The nth term is given by:

$a_{n}=a_{1}r^{n-1}$

For fifteenth term, put n=15 in above equation, we get

$a_{15}=5(-2)^{14}$

= $5{\times}16384$

= $81920$

Hence, the fifteenth term is 81920.

Option 3 is correct.

5 0

3 years ago

You are attempting to estimate the number of protester marching through the city

Alenkinab [10]

9514 1404 393

Answer:

1000

Step-by-step explanation:

If the number of protesters per minute remains a constant, then you could write the proportion ...

p/12 = 177/2.1

Multiplying by 12 gives ...

p = 12(177/2.1) ≈ 1011.4

Here, minutes are given to 2 significant figures, and the initial count is given to 3 significant figures. The best you can hope for is that your estimate is good to 3 significant figures:

1010 protesters

It is probably sufficient to report the number to 2 significant figures*:

1000 protesters

_____

* Unfortunately, with a number like 1000, the only way you can tell it has 2 significant figures is to report it as 1.0×10³ or 10. hundreds. The trailing zeros are usually not considered significant.

3 0

3 years ago