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Karo-lina-s [1.5K]
4 years ago
12

Solve for x. ​ −2(x+1/4)+1=5 ​ ​ Enter your answer as a fraction in simplest form in the box.

Mathematics
1 answer:
Advocard [28]4 years ago
5 0

Answer:

-9/4

Step-by-step explanation:

i just took the test

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Find sec 2Theta in exact value
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Answer:

sec(2\theta)=-\frac{5}{4}

Step-by-step explanation:

we know that

step 1

Find cos(\theta)

we know that

tan^2(\theta)+1=sec^2(\theta)

we have

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substitute

3^2+1=sec^2(\theta)

sec^2(\theta)=10

sec(\theta)=\pm\sqrt{10}

Remember that

Angle theta lie in Quadrant I

so

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sec(\theta)=\sqrt{10}

Remember that

sec(\theta)=\frac{1}{cos(\theta)}

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step 2

Find sin(\theta)

we know that

tan(\theta)=\frac{sin(\theta)}{cos(\theta)}

sin(\theta)=tan(\theta)cos(\theta)

we have

cos(\theta)=\frac{1}{\sqrt{10}}

tan(\theta)=3

substitute

sin(\theta)=(3)(\frac{1}{\sqrt{10}})

sin(\theta)=\frac{3}{\sqrt{10}}

step 3

Find cos(2\theta)

we know that

cos(2\theta)=2cos^2(\theta)-1

we have

cos(\theta)=\frac{1}{\sqrt{10}}

substitute

cos(2\theta)=2(\frac{1}{\sqrt{10}})^2-1

cos(2\theta)=\frac{1}{5}-1

cos(2\theta)=-\frac{4}{5}

Remember that

sec(2\theta)=\frac{1}{cos(2\theta)}

therefore

sec(2\theta)=-\frac{5}{4}

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