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Zinaida [17]
2 years ago
5

IF 0 ≤theta°≤360°find cos(2theta-10°)=-1/2

Mathematics
1 answer:
aliina [53]2 years ago
4 0

Answer:

θ

can be in the first quadrant

0

≤

θ

≤

90

or the fourth quadrant

270

≤

θ

≤

360

If

θ

is in the first quadrant,

then

sin

θ

=

5

13

cos

θ

=

12

13

tan

θ

=

5

12

Therefore,

sin

2

θ

=

2

sin

θ

cos

θ

=

2

×

5

13

×

12

13

=

120

169

cos

2

θ

=

cos

2

θ

−

sin

2

θ

=

(

12

13

)

2

−

(

5

13

)

2

=

144

169

−

25

169

=

119

169

If

θ

is in the fourth quadrant,

then

sin

θ

=

−

5

13

cos

θ

=

12

13

tan

θ

=

−

5

12

Therefore,

sin

2

θ

=

2

sin

θ

cos

θ

=

2

×

−

5

13

×

12

13

=

−

120

169

cos

2

θ

=

cos

2

θ

−

sin

2

θ

=

(

12

13

)

2

−

(

−

5

13

)

2

=

144

169

−

25

169

=

119

169

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expeople1 [14]
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0.5:3*100 =

(0.5*100):3 =

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Now we have: 0.5 is what percent of 3 = 16.666666666667

Question: 0.5 is what percent of 3?

Percentage solution with steps:

Step 1: We make the assumption that 3 is 100% since it is our output value.

Step 2: We next represent the value we seek with $x$x​.

Step 3: From step 1, it follows that $100\%=3$100%=3​.

Step 4: In the same vein, $x\%=0.5$x%=0.5​.

Step 5: This gives us a pair of simple equations:

$100\%=3(1)$100%=3(1)​.

$x\%=0.5(2)$x%=0.5(2)​.

Step 6: By simply dividing equation 1 by equation 2 and taking note of the fact that both the LHS
(left hand side) of both equations have the same unit (%); we have

$\frac{100\%}{x\%}=\frac{3}{0.5}$
100%
x%​=
3
0.5​​

Step 7: Taking the inverse (or reciprocal) of both sides yields

$\frac{x\%}{100\%}=\frac{0.5}{3}$
x%
100%​=
0.5
3​​

$\Rightarrow x=16.666666666667\%$⇒x=16.666666666667%​

Therefore, $0.5$0.5​ is $16.666666666667\%$16.666666666667%​ of $3$3​.
7 0
2 years ago
Read 2 more answers
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