Question

Can someone help me with a series of questions? I will fan and medal

Answer 1

\[\cos(\sin^{-1} \sqrt{2}/2)\]

Answer 2

\(\theta = \sin^{-1}\left(\frac{\sqrt2}{2}\right)\implies \sin(\theta)=\frac{\sqrt{2}}{2}\)

Find \(\cos(\theta)\) from this (by drawing the triangle or using an identity)

now you know the value of \(\cos(\theta)\) which means you know the value of
\[\cos\left(\sin^{-1}\left(\frac{\sqrt2}{2}\right)\right)\]

Answer 3

its \[\sqrt{2}/2 \because \pi/4, the \cos is \sqrt{2}/2\] @BAdhi

Answer 4

Yes simply it is \(\frac{1}{\sqrt{2}}\)
In this case we know that \(\sin(\theta)=\sqrt{2}/2\) gives \(\theta =45^\circ\).

But in general we do not have to find the value of the angle...

Answer 5

\[\cos^{-1} (\sin 5\pi/4)\]
How would I do this one? @BAdhi

Answer 6

Final answer should be an angle (say \(\theta\))

\(\cos^{-1}\left(\sin\left(5\pi/4\right)\right)=\theta\)
\(\sin(5\pi/4)=\cos\theta\)
\(\sin(5\pi/4)=\sin(\pi/2-\theta)\)

Find \(\theta\)

Answer 7

Sorry for asking so many questions
\[\tan(\sin^{-1} (1/3))\]
Where's sin 1/3? @BAdhi