Question #e97c2

Question

How do you use the properties of inverse trigonometric functions to evaluate $tan (arcsin (0.31))$ $tan(arcsin (0.31))$ ?
What is $sin ({sin}^{- 1} \frac{\sqrt{2}}{2})$ $\sin ( sin^{-1} frac{sqrt{2}}{2})$ ?
How do you find the exact value of $cos ({tan}^{- 1} \sqrt{3})$ $\cos(tan^{-1}sqrt{3})$ ?
How do you evaluate ${sec}^{- 1} \sqrt{2}$ $\sec^{-1} \sqrt{2}$ ?
How do you find $cos ({cot}^{- 1} \sqrt{3})$ $cos( cot^{-1} sqrt{3} )$ without a calculator?
How do you rewrite ${sec}^{2} ({tan}^{- 1} x)$ $sec^2 (tan^{-1} x)$ in terms of x?
How do you use the inverse trigonometric properties to rewrite expressions in terms of x?
How do you calculate ${sin}^{- 1} (0.1)$ $sin^-1(0.1)$ ?
How do you solve the inverse trig function ${cos}^{- 1} (- \frac{\sqrt{2}}{2})$ $cos^-1 (-sqrt2/2)$ ?
How do you solve the inverse trig function $sin ({sin}^{- 1} (\frac{1}{3}))$ $sin(sin^-1 (1/3))$ ?

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Answer 1 · 2017-04-14T16:21:28

$sin (\frac{1}{2} a r c sec 2)$ $sin(1/2arcsec2)$

$= sin (\frac{1}{2} \cdot \frac{π}{3})$ $=sin(1/2*pi/3)$

$= sin (\frac{π}{6}) = \frac{1}{2}$ $=sin(pi/6)=1/2$