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3 years ago

Given that sin(90 -5ϴ) = Cos(180 - ϴ), Find the value of ϴ

Mathematics

1 answer:

lilavasa [31]3 years ago

8 0

Answer:

30°

Step-by-step explanation:

$\because \: \sin(90 \degree - \theta) = \cos \theta \\ \therefore \: \sin(90 \degree - 5 \theta) = \cos 5\theta....(1) \\ \\ \sin(90 \degree - 5 \theta) = \cos(180 \degree - \theta)...(2) \\ from \: (1) \: and \: (2) \\ \cos 5\theta = \cos(180 \degree - \theta) \\ 5 \theta = 180 \degree - \theta \\ 5 \theta + \theta= 180 \degree \\ 6\theta= 180 \degree \\ \theta = \frac{180 \degree}{6} \\ \\ \huge \red{ \boxed{\theta = 30 \degree}}$

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2 years ago

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3 years ago

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3 years ago

Which equation represents exponential decay? * a y=3^x-4 b y=2(4)^x c y=1/2(3)^x d: y=6(1/3)^x

yuradex [85]

The equation which represents exponential decay is y= $6(1/3)^{x}$

Given four equations : 1)y= $3^{x} -4$ , 2) y= $2(4)^{x}$ , 3) y= $3^{x}/2$ , 4) y= $6(1/3)^{x}$ .

Equation is relationship between two or more variables expressed in equal to form. Equations of two variables look like ax+by=c. Exponential equation look like $a^{x}$ .

Decay means when x value increases ,the y value decreases.

We haveto put 3 values for x in the equations to check.

1)y= $3^{x} -4$

put x=0,y=-3

put x=1, y=-1

put x=2, y=5

No,itdoes not represents exponential decay.

2) y=2 $4^{x}$

put x=0,y=2

put x=1, y=8

put x=2, y=32

No,it does not represents exponential decay.

3) y= $3^{x}/2$

put x=0,y=0.5

put x=1, y=1.5

put x=2, y=4.5

No,it does not represents exponential decay.

4)y=6 $(1/3)^{x}$

put x=0,y=6

put x=1, y=2

put x=2, y=0.67

Yes ,it represents exponential decay.

Hence the equation which represents exponential decay is y=6 $(1/3)^{x}$ .

Learn more about equations at brainly.com/question/2972832

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2 years ago

Given that sin(90 -5ϴ) = Cos(180 - ϴ), Find the value of ϴ​

Given that sin(90 -5ϴ) = Cos(180 - ϴ), Find the value of ϴ