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3 years ago

∛(8+3√21) + ∛(8-3√21) solve without calculator

Mathematics

2 answers:

kykrilka [37]3 years ago

5 0

Answer:

Step-by-step explanation:

I was thinking about it and I prepared my paper and pen and started typing the problem but then I realized this...

8+ and 8-

Then I was like

OK....

Anna [14]3 years ago

3 0

Answer: 16

Step-by-step explanation:

8+3√21 + 8-3√21

= 8 +8 +3√21 -3√21

= 16

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Given that sin theta = 1/4, 0→theta→π/2, what . what is the exact value of cos 8?

natali 33 [55]

<h3>Answer: Choice B $\frac{\sqrt{15}}{4}$ </h3>

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Work Shown:

Angle theta is between 0 and pi/2, so this angle is in quadrant Q1.

Square both sides of the given equation

$\sin \theta = \frac{1}{4}\\\\\sin^2 \theta = \left(\frac{1}{4}\right)^2\\\\\sin^2 \theta = \frac{1}{16}$

Then use the pythagorean trig identity to get

$\sin^2 \theta + \cos^2 \theta = 1\\\\\cos^2 \theta = 1-\sin^2 \theta\\\\\cos \theta = \sqrt{1-\sin^2 \theta} \ \ \ \text{cosine is positive in Q1}\\\\\cos \theta = \sqrt{1-\frac{1}{16}}\\\\\cos \theta = \sqrt{\frac{16}{16}-\frac{1}{16}}\\\\\cos \theta = \sqrt{\frac{16-1}{16}}\\\\\cos \theta = \sqrt{\frac{15}{16}}\\\\\cos \theta = \frac{\sqrt{15}}{\sqrt{16}}\\\\\cos \theta = \frac{\sqrt{15}}{4}\\\\$

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