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stellarik [79]
3 years ago
7

IM STUCK PLEASE HELP

Mathematics
1 answer:
Artyom0805 [142]3 years ago
4 0

Answer:B

Step-by-step explanation:

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Find exact values for sin θ and tan θ if cos θ = -4/9 and tan θ > 0.
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Answer:

Part 1) sin(\theta)=-\frac{\sqrt{65}}{9}

Part 2) tan(\theta)=\frac{\sqrt{65}}{4}

Step-by-step explanation:

we have that

The cosine of angle theta is negative and the tangent of angle theta is positive

That means that the sine of angle theta is negative

step 1

Find sin(\theta)

we know that

sin^{2}(\theta) +cos^{2}(\theta)=1

we have

cos(\theta)=-\frac{4}{9}

substitute

sin^{2}(\theta) +(-\frac{4}{9})^{2}=1

sin^{2}(\theta) +\frac{16}{81}=1

sin^{2}(\theta)=1-\frac{16}{81}

sin^{2}(\theta)=\frac{65}{81}

square root both sides

sin(\theta)=\pm\frac{\sqrt{65}}{9}

Remember that

In this problem the sine of angle theta is negative

so

sin(\theta)=-\frac{\sqrt{65}}{9}

step 2

Find tan(\theta)

we know that

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

we have

sin(\theta)=-\frac{\sqrt{65}}{9}

cos(\theta)=-\frac{4}{9}

substitute the given values

tan(\theta)=-\frac{\sqrt{65}}{9}:-\frac{4}{9}=\frac{\sqrt{65}}{4}

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Step-by-step explanation:

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