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NikAS [45]
4 years ago
15

If sin theta=-1/4 and theta terminates in the third quadrant, find the exact value of sin2 theta.

Mathematics
2 answers:
DIA [1.3K]4 years ago
7 0

Answer:

sin(2\theta)=\frac{\sqrt{15}}{8}

Step-by-step explanation:

We are given

sin(\theta)=-\frac{1}{4}

Firstly, we can draw triangle

angle lies in third quadrant

so, we get

cos(\theta)=-\frac{\sqrt{15} }{4}

now, we can use formula

sin(2\theta)=2sin(\theta)\times cos(\theta)

now, we can plug values

sin(2\theta)=2\times -\frac{1}{4}\times -\frac{\sqrt{15} }{4}

now, we can simplify it

and we get

sin(2\theta)=\frac{\sqrt{15}}{8}

nata0808 [166]4 years ago
7 0

Answer:

\frac{\sqrt{15} }{8}  or  sqrt15/8

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