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inn [45]
2 years ago
6

BRAINLIEST!

Mathematics
2 answers:
wariber [46]2 years ago
8 0

Answer:

cosθ = - \frac{\sqrt{33}}{7}.

Step-by-step explanation:

Given  : sinθ=\frac{4}{7}.

To find : What is the exact value of cosθ in simplified  form .

Solution : We have given sinθ=\frac{4}{7}.

By the trigonometric identity : (sin)^{2} +(cos)^{2}  = 1.

Plug the value of sinθ=\frac{4}{7}.

(\frac{4}{7}) ^{2} + cos^{2} = 1.

(\frac{16}{49}) + cos^{2} = 1.

Subtracting \frac{16}{49}  from both sides

cos^{2} = 1 - \frac{16}{49}.

cos^{2} = \frac{49 -16}{49}.

cos^{2} = \frac{33}{49}.

Taking square root both sides

cos ( theta) = \sqrt{\frac{33}{49} }.

cosθ = ± \frac{\sqrt{33}}{7}.

θ lies in Quadrant II so,  cosθ = - \frac{\sqrt{33}}{7}.

Therefore, cosθ = - \frac{\sqrt{33}}{7}.

bonufazy [111]2 years ago
7 0

sin theta = 4/7

theta = arcsin (4/7)

cos (arcsin (4/7)

if theta is in the second quadrant cos theta is negative (calculators only give the postive answer)

cos (arcsin (4/7)= - sqrt(33)/7

Choice B

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