Question

1. If sin 0 = 1/√2, find the value of 0
2. If cos 0 + 2√10/7, calculate the value of sin 0.

Answer 1

For the first question, you need to find the arcsin of both sides. You can do this on a standard scientific calculator, at least on most calculators. You'll find the answer is 45 degrees: http://goo.gl/rgmeH

Answer 2

What about number 2

Answer 3

Take the arccos of both sides, and you'll find the angle is http://goo.gl/p9jqP
Then find the sine of that angle http://goo.gl/AGWsr
The answer is about .429.

Answer 4

On the other hand, maybe what's called for is the use of an identity.
Use the fact that \[\Large \sin^2\theta = 1-\cos^2\theta\]

Answer 5

I think you're supposed to do this without a calculator.

1) \(\sin \theta = \dfrac{1}{\sqrt{2}}\)

Going back to the definition of \(\sin \theta\) this means we have a triangle with opposite side = 1 and hypotenuse = \(\sqrt{2}\) as seen in drawing. From Pythagoras we can find the other leg of the triangle, and it is also 1. This means that \(\sin \theta = \cos \theta\) and the place where that happens in the first quadrant is at \(\theta = \pi/4\).

Answer 6

Is the second part supposed to be \[\cos \theta = \frac{2\sqrt{10}}{7}\]?

Answer 7

If so, the triangle looks this:

\[\sin \theta = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{3}{7}\]

Answer 8

Exact answers, no calculator needed.

Answer 9

Thank you